Deck 11: Oscillations and Waves

Question 1

Write the word or phrase that best completes each statement or answers the question.
Why does the intensity of waves from a small source decrease with the square of the distance from the source?

A) The frequency of the waves decreases as they get farther from the source.
B) The waves run out of energy as they travel.
C) The medium through which the waves travel absorbs the energy of the waves.
D) The waves slow down as they travel away from the source.
E) The waves spread out as they travel.

Answer 1

The waves spread out as they travel.

Question 2

Write the word or phrase that best completes each statement or answers the question.
Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

A) A
B) B
C) C
D) D
E) E

Answer 2

B

Question 3

Write the word or phrase that best completes each statement or answers the question.
A string of length L is under tension, and the speed of a wave in the string is What will be the speed of a wave in the string if the length is increased to 2 L but with no change in the mass or tension?

A)
B)
C)
D)
E)

Answer 3

Question 4

Write the word or phrase that best completes each statement or answers the question.
Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

A) 2T
B) T
C) T/2
D)
E)

Question 5

Write the word or phrase that best completes each statement or answers the question.
If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

A) 1750 Hz
B) 1500 Hz
C) 250 Hz
D) 750 Hz

Question 6

Write the word or phrase that best completes each statement or answers the question.
What is the wavelength of the wave shown in the figure?

A) 8 m
B) 4 m
C) 1 m
D) 2 m
E) It cannot be determined from the given information

Question 7

Write the word or phrase that best completes each statement or answers the question.
The intensity of the waves from a point source at a distance d from the source is I . What is the intensity at a distance 2d from the source?

A)
B)
C)
D)
E)

Question 8

Write the word or phrase that best completes each statement or answers the question.
When a certain string is under tension T , the speed of a wave in the string is m What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

A)
B)
C)
D)
E)

Question 9

Write the word or phrase that best completes each statement or answers the question.
What is the frequency of the wave shown in the figure?

A) 4 Hz
B) 0.5 Hz
C) 2 Hz
D) 1 Hz
E) It cannot be determined from the given information

Question 10

Write the word or phrase that best completes each statement or answers the question.
The intensity of the waves from a point source at a distance d from the source is I . At what distance from the sources is the intensity equal to 2I?

A)
B)
C)
D)

Question 11

Write the word or phrase that best completes each statement or answers the question.
A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?

A)
B)
C)
D)
E)

Question 12

Write the word or phrase that best completes each statement or answers the question.
An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of Oscillation of the object?

A) T/4
B) T
C) 2T
D) 4T
E) T/2

Question 13

Write the word or phrase that best completes each statement or answers the question.
The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a Function of time?

A) graph a
B) graph b
C) graph c
D) graph d

Question 14

Write the word or phrase that best completes each statement or answers the question.
When a guitar is tuned to adjust it pitch, what is it that is changed?

A) The wavelength of the fundamental.
B) The amplitude of the fundamental.
C) The frequency of the fundamental.

Question 15

Write the word or phrase that best completes each statement or answers the question.
A string of mass m is under tension, and the speed of a wave in the string is What will be the speed of a wave in the string if the mass of the string is increased to 2 m but with no change in the length or tension?

A)
B)
C)
D)
E)

Question 16

Write the word or phrase that best completes each statement or answers the question.
Four waves are described by the following equations, where distances are measured in meters and times in seconds.

Which of these waves have the same period?

A) I and II, and also III and IV
B) I and III, and also II and IV
C) I and IV, and also II and III
D) All of them have the same period.
E) They all have different periods.

Question 17

Write the word or phrase that best completes each statement or answers the question.
The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a Function of time?

A) graph a
B) graph b
C) graph c
D) graph d

Question 18

Write the word or phrase that best completes each statement or answers the question.
Four waves are described by the following equations, where distances are measured in meters and times in seconds.

Which of these waves have the same speed?

A) II and IV
B) I and II
C) I and III
D) III and IV
E) II and III

Question 19

Write the word or phrase that best completes each statement or answers the question.
The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a
Function of time?

A) graph a
B) graph b
C) graph c
D) graph d

Question 20

Write the word or phrase that best completes each statement or answers the question.
A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the Greatest?

A) A and D
B) B
C) A and C
D) A and B
E) C

Question 21

Choose the one alternative that best completes the statement or answers the question.
The position of an air-track cart that is oscillating on a spring is given by the equation x=(12.4 cm)
At what value of t after t=0.00 s is the cart first located at x=8.47 cm?

A) 4.34 s
B) 0.129 s
C) 7.39 s
D) 0.108 s
E) 7.75 s

Question 22

Choose the one alternative that best completes the statement or answers the question.
An object is oscillating on a spring with a period of 4.60 s. At time t=0.00 s the object has zero speed and is at x=8.30 cm. What is the acceleration of the object at t=2.50 s?

A)
B)
C)
D)
E)

Question 23

Choose the one alternative that best completes the statement or answers the question.
If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

A) 2
B) 4
C) It does not change.
D) 1/2
E) 1/4

Question 24

Choose the one alternative that best completes the statement or answers the question.
The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

A) 0.191 ms
B)
C)
D)
E)

Question 25

Choose the one alternative that best completes the statement or answers the question.
If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?

A) 4
B) 2
C)
D)

Question 26

Write the word or phrase that best completes each statement or answers the question.
The position of an object that is oscillating on an ideal spring is given by x=(17.4 cm)
Write an expression for the velocity of the particle as a function of time using the sine function.

Question 27

Choose the one alternative that best completes the statement or answers the question.
An object undergoing simple harmonic motion has a maximum displacement of 6.2 m at t=0.00 s. If the angular frequency of oscillation is 1.6 rad/s, what is the object's displacement when t=3.5 s?

A) 3.7 m
B) 5.6 m
C) 3.1 m
D) 4.8 m

Question 28

Write the word or phrase that best completes each statement or answers the question.
If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you,
what are the frequency and period of the wave?

Question 29

Write the word or phrase that best completes each statement or answers the question.
A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x , as a function of time t , if x is equal to 8.3 cm at t= 0.0 s. Use the cosine function.

Question 30

Choose the one alternative that best completes the statement or answers the question.
If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

A) 2
B) 4
C) It does not change.
D) 1/2
E) 1/4

Question 31

Choose the one alternative that best completes the statement or answers the question.
A package is oscillating on a spring scale with a period of 4.60 s. At time t=0.00 s the package has zero speed and is at x=8.30 cm. At what time after t=0.00 s will the package first be at x=4.15 cm?

A) 0.767 s
B) 1.30 s
C) 1.15 s
D) 0.575 s
E) 1.53 s

Question 32

Write the word or phrase that best completes each statement or answers the question.
A point on the string of a violin moves up and down in simple harmonic motion with an
amplitude of 1.24 mm and a frequency of 875 Hz.
(a) What is the maximum speed of that point in SI units?
(b) What is the maximum acceleration of the point in SI units?

Question 33

Choose the one alternative that best completes the statement or answers the question.
An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. At time t=0.00 s the cart is released at the position x=+0.250 m. What is the position of the cart when t=29.6 s ?

A) x=0.218 m
B) x=0.0461 m
C) x=0.210 m
D) x=0.342 m
E) x=-0.218 m

Question 34

Write the word or phrase that best completes each statement or answers the question.
If a pendulum makes 12 complete swings in 8.0 s, what are its (a) frequency and (b)
period?

Question 35

Write the word or phrase that best completes each statement or answers the question.
The position of an object that is oscillating on a spring is given by the equation x = (18.3
cm) cos[(2.35 s-1)t]. What are the (a) frequency, (b) amplitude, and (c) period of this
motion?

Question 36

Write the word or phrase that best completes each statement or answers the question.
A sewing machine needle moves up and down in simple harmonic motion with an
amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and
(b) maximum acceleration of the tip of the needle?

Question 37

Write the word or phrase that best completes each statement or answers the question.
The position of an object that is oscillating on an ideal spring is given by x=(17.4 cm)
Write an expression for the acceleration of the particle as a function of time using the cosine function.

Question 38

Write the word or phrase that best completes each statement or answers the question.
An object oscillates such that its position x as a function of time t obeys the equation where t is in seconds.
(a) In one period, what total distance does the object move?
(b) What is the frequency of the motion?
(c) What is the position of the object when t=1.00 s?

Question 39

Write the word or phrase that best completes each statement or answers the question.
A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz
and an amplitude of 1.27 cm.
(a) How long does it take the tip of the needle to move from the highest point to the lowest
point in its travel?
(b) How long does it take the needle tip to travel a total distance of 11.43 cm?

Question 40

Write the word or phrase that best completes each statement or answers the question.
The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm)
cos[(1.26 s-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

Question 41

Choose the one alternative that best completes the statement or answers the question.
An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. The object has a maximum displacement at t=0.00 s of 0.232 m. If the force constant (spring constant) is 29.8 N/m, what is the potential energy stored in the mass-spring system when t=1.42 s?

A) 0.399 J
B) 0.256 J
C) 0.329 J
D) 0.350 J

Question 42

Choose the one alternative that best completes the statement or answers the question.
In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale?

A) 410 N/m
B) 820 N/m
C) 330 N/m
D) 600 N/m
E) 650 N/m

Question 43

Write the word or phrase that best completes each statement or answers the question.
The equation of motion of a particle undergoing simple harmonic motion in the y direction is
At time t=0.60 s determine the particle's (a) position, (b) velocity, and (c) acceleration.

Question 44

Choose the one alternative that best completes the statement or answers the question.
A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?

A) 12.1 N/m
B) 0.610 N/m
C) 2.45 N/m
D) 24.1 N/m
E) 0.102 N/m

Question 45

Choose the one alternative that best completes the statement or answers the question.
A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where
If the force constant (spring constant) of the spring is 12 N/m, find the period of oscillation of this setup on a planet where

A) 4.36 s
B) 5.70 s
C) 3.35 s
D) 2.51 s

Question 46

Write the word or phrase that best completes each statement or answers the question.
A 1.15-kg beaker (including its contents) is placed on a vertical spring scale. When the system is sent into vertical vibrations, it obeys the equation
What is the force constant (spring constant) of the spring scale, assuming it to be ideal?

Question 47

Choose the one alternative that best completes the statement or answers the question.
A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t=0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of closest to
The mass of the block is

A) 2.6 kg
B) 9.4 kg
C) 2.3 kg
D) 4.7 kg

Question 48

Choose the one alternative that best completes the statement or answers the question.
When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

A) 0.286 s
B) 1.44 s
C) 0.695 s
D) 0.0769 s
E) 0.483 s

Question 49

Choose the one alternative that best completes the statement or answers the question.
A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations?

A) 1.14 s
B) 1.29 s
C) 0.263 s
D) 0.527 s
E) 2.57 s

Question 50

Choose the one alternative that best completes the statement or answers the question.
A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) What is the oscillation angular frequency of the block if

A) 0.40 rad/s
B) 0.56 rad/s
C) 3.5 rad/s
D) 2.5 rad/s

Question 51

Choose the one alternative that best completes the statement or answers the question.
A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car?

A) 1900 kg
B) 920 kg
C) 990 kg
D) 890 kg
E) 760 kg

Question 52

Choose the one alternative that best completes the statement or answers the question.
If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?

A) 2
B) 4
C) It does not change.
D) 1/2
E) 1/4

Question 53

Choose the one alternative that best completes the statement or answers the question.
An object of mass m=8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The spring stretches 2.2 cm before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency?

A)
B) 1.6 Hz
C) 3.4 Hz
D) 0.52 Hz

Question 54

Choose the one alternative that best completes the statement or answers the question.
A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 450 N/m. The block is pulled from its equilibrium position at x=0.000 m to a position x=+0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x -axis. The maximum elastic potential energy of the system is closest to

A) 1.8 J
B) 1.7 J
C) 1.4 J
D) 1.3 J
E) 1.6 J

Question 55

Choose the one alternative that best completes the statement or answers the question.
A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 570 N/m. The block is pulled from its equilibrium position at x=0.000 m to a displacement x=+0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x -axis. When the position of the block is x=0.057 m, its kinetic energy is closest to

A) 1.1 J
B) 0.95 J
C) 0.84 J
D) 1.0 J
E) 0.90 J

Question 56

Choose the one alternative that best completes the statement or answers the question.
A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

A) 1.4 Hz
B) 4.6 Hz
C) 2.3 Hz
D) 3.2 Hz

Question 57

Choose the one alternative that best completes the statement or answers the question.
A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 360 N/m. The block is pulled from its equilibrium position at x=0.000 m to a position x=+0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x -axis. When the position is x=-0.037 m, what is the acceleration of the block?

A)
B)
C)
D)
E)

Question 58

Choose the one alternative that best completes the statement or answers the question.
A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface. At time t=0.00 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of The force constant (spring constant) of the spring is closest to

A) 13 N/m
B) 12 N/m
C) 15 N/m
D) 11 N/m
E) 14 N/m

Question 59

Choose the one alternative that best completes the statement or answers the question.
A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant (force constant) of the bungee cord?

A) 26.1 N/m
B) 19.6 N/m
C) 16.3 N/m

Question 60

Write the word or phrase that best completes each statement or answers the question.
When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (spring constant) of 467 N/m, the system obeys the equation y=(4.4 cm) What is the mass of this laboratory sample?

Question 61

Write the word or phrase that best completes each statement or answers the question.
If both the mass of a simple pendulum and its length are doubled, the period will

A) be unchanged.
B) increase by a factor of
C) increase by a factor of 4 .
D) increase by a factor of 2 .
E) increase by a factor of

Question 62

Write the word or phrase that best completes each statement or answers the question.
Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he
makes 30 complete swings in 2.4 minutes.
(a) What is the frequency (in hertz) of Tarzan's swing?
(b) How long is the vine he is using?

Question 63

Write the word or phrase that best completes each statement or answers the question.
The period of a simple pendulum that is 1.00 m long on another planet is 1.66 s. What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg?

A)
B)
C)
D)

Question 64

Write the word or phrase that best completes each statement or answers the question.
An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant) 1720 N/m . The object is set into simple harmonic motion, with an initial velocity of and an initial displacement of Calculate the maximum speed the object raches during its motion.

Question 65

Write the word or phrase that best completes each statement or answers the question.
A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be?

A)
B) T
C)
D) 3T
E) T/3

Question 66

Write the word or phrase that best completes each statement or answers the question.
A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing?

A) 6.00 s
B) 2.00 s
C) 3.46 s
D) 1.15 s
E) 0.667 s

Question 67

Write the word or phrase that best completes each statement or answers the question.
A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box. The larger box is attached to an ideal spring of force constant (spring constant) 150 N/m, as shown in the figure. Find
(a) the amplitude of the resulting oscillations of this system,
(b) the frequency of the oscillations and
(c) the period of the oscillations.

Question 68

Choose the one alternative that best completes the statement or answers the question.
An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid?

A)
B)
C)
D)
E)

Question 69

Write the word or phrase that best completes each statement or answers the question.
A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period?

A)
B)
C) T
D) 2T
E) T/2

Question 70

Write the word or phrase that best completes each statement or answers the question.
A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on
a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a
speed of 1.5 m/s at the equilibrium position.
(a) What is the amplitude of vibration?
(b) At what distance from the equilibrium position are the kinetic energy and the potential
energy the same?

Question 71

Write the word or phrase that best completes each statement or answers the question.
On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon?

A) T/3
B)
C) 6T
D) T/6
E)

Question 72

Write the word or phrase that best completes each statement or answers the question.
A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m
along a horizontal, frictionless surface. The object oscillates in simple harmonic motion
and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and
(b) the amplitude of vibration of the system?

Question 73

Write the word or phrase that best completes each statement or answers the question.
A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the
spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down
and released from rest.
(a) How long does it take the wood to make 3 complete cycles of vibration?
(b) How much total mechanical energy does this system contain if we choose the total
potential energy (elastic and gravitational) to be zero at the equilibrium position of the
hanging block?

Question 74

Write the word or phrase that best completes each statement or answers the question.
A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet?

Question 75

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is 19 N/m. (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

Question 76

Choose the one alternative that best completes the statement or answers the question.
A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period?

A) T
B)
C)
D) T/2
Е) 2T

Question 77

Write the word or phrase that best completes each statement or answers the question.
A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m
oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest
at position x = 10 cm from the equilibrium position.
(a) What is the frequency of the oscillations of the cart?
(b) Determine the maximum speed of the cart. Where does the maximum speed occur?
(c) Find the maximum acceleration of the mass. Where does the maximum acceleration
occur?
(d) How much total energy does this oscillating system contain?
(e) Express the displacement as a function of time using a cosine function.

Question 78

Write the word or phrase that best completes each statement or answers the question.
When a certain simple pendulum is set swinging, its angular displacement as a function of time t obeys the equation
How long is the pendulum?

Question 79

Choose the one alternative that best completes the statement or answers the question.
An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N-40 ?

A)
B)
C)
D)
E)

Question 80

Write the word or phrase that best completes each statement or answers the question.
A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches
the spring 2.0 cm downward. The stone is then pulled an additional distance of 1.0 cm
down and released from rest.
(a) Write down the equation for the vertical position y of the stone as a function of time t,
using the cosine function. Take the origin at the equilibrium point of the stone, with the
positive y direction upward.
(b) How fast is the stone moving at a time equal to 1/3 of its period of motion?