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Physics Harmonic Motion

Total questions: 40

Worksheet time: 1hrs 19mins

Name
Class
Date
1.

Which of the following is/ are characteristics of simple harmonic motion?

I. The acceleration is constant .

II. The restoring force is proportional to the displacement.

III. The frequency is independent of the amplitude.

a)

II only

b)

I and II only

c)

I and III only

d)

II and III only

e)

I, II, and III

2.

What combination of values will result in a spring - block system with the greatest frequency?

a)

A = 50 cm; k = 80 N/m; m = 2 kg

b)

A = 50 cm; k = 100 N/m; m = 2 kg

c)

A = 50 cm; k = 100 N/m; m = 4 kg

d)

A = 75 cm; k = 80 N/m; m = 2kg

e)

A = 75 cm; k = 100 N/m; m = 4 kg

3.

A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x = 0) with amplitude A. What fraction of the total energy is in the form of kinetic energy when the block is at position

(x =1/2 A)?

a)

1/3

b)

3/8

c)

1/2

d)

2/3

e)

3/4

4.

A linear spring of force constant k is used in physics lab experiment. A block of mass m is attached to the spring and the resulting frequency, f, of the simple harmonic oscillation is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If f2 is plotted versus 1/m, the graph will be a straight line with slope

a)

4π2/k2

b)

4π2/k

c)

(4π)(2k)

d)

k/4π2

e)

k2/4π2

5.

A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5o and period T. If the same pendulum is given a maximum angular displacement of 10o, then which of the following best gives the period of the oscillations?

a)

T/2

b)

T/√2

c)

T

d)

T√2

e)

2T

6.

A mass of 200. g stretches a spring 10.0 cm. The spring is then stretched an additional 5.00 cm and released. Determine the max velocity.

a)

0.495 m/s

b)

0.248 m/s

c)

0.371 m/s

d)

0.742 m/s

7.

The period of a simple pendulum is 2.00 sec. Find the length of the pendulum.

a)

1.99 m

b)

0.632 m

c)

0.993 m

d)

1.41 m

8.

A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude A on the end of an ideal spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will

a)

decrease by a factor of 4

b)

decrease by a factor of 2

c)

decrease by a factor of √2

d)

remain the same

e)

increase by a factor of 2

9.

A spring with a natural length 40 cm and a spring constant of 400 N/m is hung vertically with a 10 kg mass attached to the end. Assuming the spring's mass is negligible, what will be the final length of the spring when it reaches equilibrium?

a)

25 cm

b)

35 cm

c)

40 cm

d)

50 cm

e)

65 cm

10.
A force of  30 N stretches a very light ideal spring 0.73 m from equilibrium. What is the force constant (spring constant) of the spring?
a)
41 N/m
b)
22 N/m
c)
34 N/m
d)
46 N/m
11.
A pendulum is 0.75 meters long and has a period of 4.17 seconds. The Pendulum is on an unknown planet.  What is the gravity of the Unknown Planet?
a)
9.8
b)
3.4
c)
1.7
d)
Greater than 9.8
12.

From the graph ,the spring constant is.

a)

4.5 N/m

b)

15 N/m

c)

20 N/m

d)

200 N/m

13.
A mass-spring system can oscillate with simple harmonic motion because a compressed or stretched spring has which kind of energy?
a)
kinetic
b)
mechanical
c)
gravitational potential
d)
elastic potential
14.
The period of a pendulum may be decreased by
a)
Increasing the mass of the bob
b)
moving the equilibrium point
c)
decreasing the mass of the bob
d)
shortening the length of pendulum
15.
In any system in SHM, the restoring force acting on the mass in the system is proportional to
a)
the displacement
b)
the length of the pendulum
c)
the mass
d)
the frequency
16.

The variation of the acceleration, a of a particle executing SHM with displacement, x is as shown in figure:

a)
b)
c)
d)
17.

The displacement x, for a particle at time t in simple harmonic motion is given by the equation, x = 10 sin 20t where x is in meters and t is in seconds. Determine the displacement at t=10 s

a)

91.3 m

b)

8.73 m

c)

-91.3 m

d)

-8.73 m

18.
Two pendulums are in simple harmonic motion.  Pendulum A is longer than pendulum B.  Pendulum A has a larger mass than B.  The period of pendulum A is
a)
longer than pendulum B
b)
shorter than pendulum B
c)
the same as pendulum B
d)
not enough information
19.

A pendulum swinging with a maximum amplitude of π/6 has a period of T. If the maximum amplitude is increased to π/3, what is the new period of the pendulum?

a)

T/4

b)

T/2

c)

T

d)

2T

20.

A pendulum's period is initially t. Changes are made to the system so that the new period is 2t. What may have been changed?

a)

The length of the pendulum was increased by a factor of 2.

b)

The pendulum was moved to a planet with 2 times the mass of Earth.

c)

The length of the pendulum was increased by a factor of 4.

d)

The pendulum was moved to a planet with 4 times the mass of earth.

21.

The energy contained in a pendulum depends on its

I. period

II. amplitude

III. mass

a)

I only

b)

II only

c)

II and III only

d)

I, II, and III

22.
Which of the following is true of a damped simple pendulum in which the amplitude of motion decreases exponentially?
a)
Its period decreases through time.
b)
The total energy of the pendulum remains the same.
c)
The maximum kinetic energy decreases through time.
d)
The maximum potential energy increases through time.
23.
The energy contained in a pendulum depends on its
I. period
II. amplitude
III. mass
a)
I only
b)
II only
c)
II and III only
d)
I, II, and III
24.
A pendulum swinging with a maximum amplitude of π/6 has a period of T.  What must happen for the period to remain the same if the amplitude of motion is doubled?
a)
The length must be increased by a factor of 2.
b)
The length must be increased by a factor of 4.
c)
The acceleration due to gravity must be decreased by a factor of 2.
d)
The length and acceleration due to gravity must remain the same.
25.
Which position shows the spring with maximum kinetic energy?
a)
A
b)
B
c)
C
d)
D
26.

The maximum displacement from equilibrium of a particle is 1 m and its maximum acceleration is

1.57 m s-2. The period of the particle will be

a)

1.25 s

b)

0.63 s

c)

0.20 s

d)

5.03 s

27.

The acceleration of a particle in SHM is:

a)

always zero

b)

always constant

c)

maximum at amplitude

d)

maximum at the equilibrium position

28.

The amplitude and period in a SHM is 0.5 m and 0.4 s respectively. The equation of SHM will be:

a)

x=0.5 sin 5πt

b)

x=0.5 sin 4πt

c)

x=0.5 sin 2.5πt

d)

x=0.5 sin 0.8πt

29.

The graph in FIGURE 1 shows the relationship between the acceleration, a and its displacement, x for an object of mass 2 kg which is in simple harmonic motion. Determine the frequency of oscillation.

a)

1.6 Hz

b)

1.26 Hz

c)

0.20 Hz

d)

5.00 Hz

30.

A mass-spring system can oscillate with simple harmonic motion because a compressed or stretched spring can store which kind of energy?

a)

kinetic

b)

mechanical

c)

gravitational potential

d)

elastic potential

31.
An object oscillating in simple harmonic motion has a time period T. The first graph shows how its displacement varies with time. Which of the subsequent graphs, A to D, show how the kinetic energy, Ek, of the object varies with time? 
a)
A
b)
B
c)
C
d)
D
32.
The diagram shows a velocity-time graph for a mass moving up and down on the end of a spring. Which point represents the velocity of the mass when at the lowest point of its motion? 
a)
A
b)
B
c)
C
d)
D
33.
A mass-spring system is set into simple harmonic motion. Which graph shows the variation of the acceleration, a, of the mass with its displacement, x? 
a)
A
b)
B
c)
C
d)
D
34.
A mass M hangs in equilibrium on a spring. M is made to oscillate about the equilibrium position by pulling it down 10 cm and releasing it. The time for M to travel back to the equilibrium position for the first time is 0.50 s. Which row, A to D, in the table is correct for these oscillations? 
a)
A
b)
B
c)
C
d)
D
35.
The period of vertical oscillation of a mass-spring system is T when the spring carries a mass of 1.00 kg. What mass should be added to the 1.00 kg if the period is to be increased to 1.50 T ? 
a)
0.25 kg 
b)
1.00 kg 
c)
1.25 kg 
d)
2.00 kg 
36.
Which graph, A to D, shows the variation of the kinetic energy, Ek, with displacement x for a particle performing simple harmonic motion? 
a)
A
b)
B
c)
C
d)
D
37.
The time period of oscillation of a simple pendulum of length l is the same as the time period of oscillation of a mass M attached to a vertical spring. The length and mass are then changed.
Which row, A to D, in the table would give a simple pendulum with a time period twice that of the spring oscillations? 
a)
A
b)
B
c)
C
d)
D
38.
The frequency of a body moving with simple harmonic motion is doubled. If the amplitude remains the same, which one of the following is also doubled? 
a)
the time period  
b)
the total energy
c)
 the maximum velocity 
d)
the maximum acceleration
39.
The time period of a pendulum on Earth is 1.0 s. What would be the period of a pendulum of the same length on a planet with half the density but twice the radius of Earth? 
a)
0.5s  
b)
1.0s
c)
1.4s
d)
2.0s
40.
A mass is hung from a spring and set into vertical oscillation.
Which row in the table correctly shows the kinetic energy Ek of the mass at maximum displacement and the potential energy Ep of the mass at the equilibrium position?
a)
A
b)
B
c)
C
d)
D

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