Question 1

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 N/m.The block is pulled from its equilibrium position at x = 0.00 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 displacement is x = 0.024 m,what is the kinetic energy of the block?
A) 0.44 J
B) 0.41 J
C) 0.46 J
D) 0.49 J
E) 0.52 J

Accepted Answer

The answer of A 0.025-kg block on a horizontal frictionless...

Question 2

A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table.The spring is aligned along the x-axis and is fixed to a peg in the table.Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s,and the two masses stick together.What are the amplitude and period of the oscillations that result from this collision?
A) 0.300 m, 1.26 s
B) 0.300 m, 0.889 s
C) 0.424 m, 0.889 s
D) 0.424 m, 1.26 s
E) 0.424 m, 5.00 s

Accepted Answer

The answer of A 2.00-kg object is attached to an...

Question 3

In the figure,two masses,M = 16 kg and m = 12.8.0 kg,are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m.The system is set into oscillation with an amplitude of 78 cm.At the instant when the acceleration is at its maximum,the 16-kg mass separates from the 12.8.0-kg mass,which then remains attached to the spring and continues to oscillate.What will be the amplitude of oscillation of the 12.8.0-kg mass? 
A) 78 cm
B) 62 cm
C) 35 cm
D) 98 cm
E) 180 cm

Accepted Answer

The answer of In the figure,two masses,M = 16 kg...

Question 4

A frictionless simple pendulum on Earth has a period of 1.75 s.On Planet X its period is 2.14 s.What is the acceleration due to gravity on Planet X?

Accepted Answer

The answer of A frictionless simple pendulum on Earth has...

Question 5

A lightly damped harmonic oscillator,with a damping force proportional to its speed,is oscillating with an amplitude of 0.500 cm at time t = 0.When t = 8.20 s,the amplitude has died down to 0.400 cm.At what value of t will the oscillations have an amplitude of 0.250 cm?
A) 18.5 s
B) 20.5 s
C) 16.5 s
D) 25.5 s
E) 5.13 s

Accepted Answer

The answer of A lightly damped harmonic oscillator,with a damping...

Question 6

A large stick is pivoted about one end and allowed to swing back and forth with no friction as a physical pendulum.The mass of the stick is 5.40 kg and its center of gravity (found by finding its balance point)is 1.80 m from the pivot.If the period of the swinging stick is 6.90 seconds,what is the moment of inertia of the stick about an axis through the pivot?

Accepted Answer

The answer of A large stick is pivoted about one...

Question 7

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls,as shown in the figure.What is angular frequency of the oscillation if k₁ = 7.6 N/m and k₂ = 5.0 N/m? A) 2.5 rad/s B) 3.5 rad/s C) 0.40 rad/s D) 0.56 rad/s

Accepted Answer

The answer of A 2.0 kg block on a frictionless...

Question 8

In the figure,a 0.24-kg ball is suspended from a very light string 9.79 m long and is pulled slightly to the left.As the ball swings without friction through the lowest part of its motion it encounters an ideal massless 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 of the spring is 21 N/m.(Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

Accepted Answer

The answer of In the figure,a 0.24-kg ball is suspended...

Question 9

A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal,frictionless track. At time t = 0.00 s,the mass is released from rest at x = 10.0 cm. (That is,the spring is stretched by 10.0 cm.)
(a)Find the frequency of the oscillations.
(b)Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur?
(c)What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur?
(d)Determine the total energy of the oscillating system.
(e)Express the displacement x as a function of time t.

Accepted Answer

The answer of A 1.5-kg mass attached to an ideal...

Question 10

A uniform meter stick is freely pivoted about the 0.20-m mark.If it is allowed to swing in a vertical plane with a small amplitude and friction,what is the frequency of its oscillations?
A) 0.55 Hz
B) 0.66 Hz
C) 0.92 Hz
D) 1.1 Hz
E) 1.3 Hz

Accepted Answer

The frequency of oscillations of a simple pendulum is given by the formula f=1/(2π)√(g/L), where L is the length of the pendulum and g is the acceleration due to gravity. In this case, the meter stick will act as a simple pendulum with L=0.80 m (distance from pivot to end of stick) and g=9.81 m/s^2. Plugging these values into the formula, we get f=1/(2π)√(9.81/0.80)≈0.66 Hz. Therefore, the best choice is B.

Question 11

A 0.50-kg object is attached to an ideal massless spring of spring 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.
(a)What is the amplitude of vibration?
(b)At what location are the kinetic energy and the potential energy of the system the same?

Accepted Answer

The answer of A 0.50-kg object is attached to an...

Question 12

A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 500 N/m.The block is pulled from its equilibrium position at x = 0.00 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 displacement is x = -0.052 m,find the acceleration of the block. A) 92 m/s² B) 46 m/s² C) 69 m/s² D) 230 m/s² E) 280 m/s²

Accepted Answer

The equation for the total energy of a mass-spring system is given by:

E = 1/2 k x^2

Where E is the energy, k is the spring constant, and x is the displacement from equilibrium.

At the point where the block is pulled to a displacement of +0.080 m, the energy stored in the spring is:

E = 1/2 (500 N/m) (0.080 m)^2
E = 1.28 J

Since the block is released from rest, all of this energy is initially in the form of potential energy. At the point where the block has moved to a displacement of -0.052 m, all of this energy will be in the form of kinetic energy, since the block has gone through its equilibrium position and is now moving in the opposite direction.

Therefore, we can set the potential energy at the initial displacement equal to the kinetic energy at the final displacement:

1/2 k x1^2 = 1/2 mv2^2

where x1 is the initial displacement (0.080 m), v2 is the velocity at the final displacement (-0.052 m), and m is the mass of the block (0.28 kg).

Solving for v2, we get:

v2 = sqrt[(k/m) x1^2]

v2 = sqrt[(500 N/m) / (0.28 kg)] (0.080 m)

v2 = 1.13 m/s

Since the block is moving in the opposite direction, the acceleration is given by:

a = -kx / m

At the final displacement of -0.052 m, the acceleration is:

a = -(500 N/m) (-0.052 m) / 0.28 kg

a = 92 m/s^2

Therefore, the answer is A.

Question 13

A long thin uniform rod of length 1.50 m is to be suspended from a frictionless pivot located at some point along the rod so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be located?
A) 7.98 cm
B) 7.52 cm
C) 8.73 cm
D) 8.40 cm
E) 23.4 cm

Accepted Answer

The answer of A long thin uniform rod of length...

Question 14

A 56.0 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 of the bungee cord,assuming it has negligible mass compared to that of the jumper?
A) 17.6 N/m
B) 21.1 N/m
C) 28.2 N/m

Accepted Answer

The answer of A 56.0 kg bungee jumper jumps off...

Question 15

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m.The object is Calculate the maximum speed the object reaches during its motion.

Accepted Answer

The answer of An object of mass 6.8 kg is...

Question 16

A 2.25-kg object is attached to a horizontal an ideal massless spring on a frictionless table.What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4.50 cm?

Accepted Answer

The answer of A 2.25-kg object is attached to a...

Question 17

An object weighing 44.1 N hangs from a vertical massless ideal spring.When set in vertical motion,the object obeys the equation y(t)= (6.20 cm)cos[(2.74 rad/s)t - 1.40].
(a)Find the time for this object to vibrate one complete cycle.
(b)What are the maximum speed and maximum acceleration of the object?
(c)What is the TOTAL distance the object moves through in one cycle?
(d)Find the maximum kinetic energy of the object.
(e)What is the spring constant of the spring?

Accepted Answer

The answer of An object weighing 44.1 N hangs from...

Question 18

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J.If the oscillation amplitude is 20.0 cm,what is the oscillation frequency?
A) 4.5 Hz
B) 1.4 Hz
C) 2.3 Hz
D) 3.2 Hz

Accepted Answer

The answer of A 0.25 kg ideal harmonic oscillator has...

Question 19

A 1.6-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m.The block is pulled from its equilibrium position at x = 0.00 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.What is the velocity of the block at time t = 0.40 s?
A) 0.82 m/s
B) -0.82 m/s
C) 0.30 m/s
D) -0.30 m/s
E) 0.00 m/s

Accepted Answer

The answer of A 1.6-kg block on a horizontal frictionless...

Question 20

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?
A) 20.0 cm
B) 167 cm
C) 30.0 cm
D) 0.00 cm
E) 26.7 cm

Accepted Answer

The amplitude of a lightly damped harmonic oscillator decreases exponentially over time. Given that the amplitude decreases from 60.0 cm to 40.0 cm in 10.0 s, it means that after another 10.0 s, the amplitude will decrease by the same factor, which is 40.0/60.0 = 2/3. Therefore, after another 10.0 s, the amplitude will be 2/3 of 40.0 cm, which is approximately 26.7 cm.

Quiz 1: A: Foundations

A frictionless simple pendulum on Earth has a period of 1.75 s.On Planet X its period is 2.14 s.What is the acceleration due to gravity on Planet X?

A lightly damped harmonic oscillator,with a damping force proportional to its speed,is oscillating with an amplitude of 0.500 cm at time t = 0.When t = 8.20 s,the amplitude has died down to 0.400 cm.At what value of t will the oscillations have an amplitude of 0.250 cm?

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls,as shown in the figure.What is angular frequency of the oscillation if k1 = 7.6 N/m and k2 = 5.0 N/m?

A uniform meter stick is freely pivoted about the 0.20-m mark.If it is allowed to swing in a vertical plane with a small amplitude and friction,what is the frequency of its oscillations?

A long thin uniform rod of length 1.50 m is to be suspended from a frictionless pivot located at some point along the rod so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be located?

A 56.0 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 of the bungee cord,assuming it has negligible mass compared to that of the jumper?

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m.The object is Calculate the maximum speed the object reaches during its motion.

A 2.25-kg object is attached to a horizontal an ideal massless spring on a frictionless table.What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4.50 cm?

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J.If the oscillation amplitude is 20.0 cm,what is the oscillation frequency?

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls,as shown in the figure.What is angular frequency of the oscillation if k₁ = 7.6 N/m and k₂ = 5.0 N/m?