Question 1

If both the mass of a simple pendulum and its length are doubled, the period will

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Question 2

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?

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Question 3

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?

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Question 4

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.

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Question 5

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?

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Question 6

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?

Accepted Answer

The period $T$ of a simple pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity. Tripling the length of the pendulum ($L$ becomes $3L$) results in a new period $T' = 2\pi\sqrt{\frac{3L}{g}}$. This can be simplified to $T' = \sqrt{3}T$. Given that $T = 2.00$ s, $T' = \sqrt{3} \times 2.00$ s $= 3.46$ s.

Question 7

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.

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Question 8

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?

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Question 9

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?

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Question 10

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?

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Question 11

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?

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Question 12

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?

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Question 13

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?

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Question 14

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?

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Question 15

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.)

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Question 16

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?

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Question 17

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.

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Question 18

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?

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Question 19

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  ?

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Question 20

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?

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Quiz 11: Oscillations and Waves

If both the mass of a simple pendulum and its length are doubled, the period will

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?

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?

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.

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 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 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?

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 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?

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?

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 ?