Simple Harmonic Motion  Multiple Choice Questions
Q1. 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 line, A to D, is correct for these oscillations?

Amplitude /cm 
Period /s 
A 
10 
1.0 
B 
10 
2.0 
C 
20 
2.0 
D 
20 
1.0 
Q2. A particle oscillates with undamped simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?
A 
It is least when the speed is greatest. 
B 
It is always in the opposite direction to its velocity. 
C 
It is proportional to the frequency. 
D 
It decreases as the potential energy increases. 
Q3. Which one of the following statements is true when an object performs simple harmonic motion about a central point O?
A 
The acceleration is always away from O. 
B 
The acceleration and velocity are always in opposite directions. 
C 
The acceleration and the displacement from O are always in the same direction. 
D 
The graph of acceleration against displacement is a straight line. 
Q4. A particle of mass m executes simple harmonic motion in a straight line with amplitude A and frequency f. Which one of the following expressions represents the total energy of the particle?
Q5. A body moves with simple harmonic motion of amplitude A and frequency b/2 .
What is the magnitude of the acceleration when the body is at maximum displacement?
Q6. A simple pendulum and a massspring system are taken to the Moon, where the gravitational field strength is less than on Earth.
Which line, A to D, correctly describes the change, if any, in the period when compared with its value on Earth?

period of pendulum 
period of massspring system 
A 
decrease 
decrease 
B 
increase 
increase 
C 
no change 
decrease 
D 
increase 
no change 
Q7. A simple pendulum and a massspring system both have the same time period T at the surface of the Earth. If taken to another planet where the acceleration due to gravity was half that on Earth, which line, AD, in the table gives correctly the new periods?

simple pendulum 
massspring 
A 

T 
B 

T 
C 


D 


Q8. Which one of the following statements is not true for a body vibrating in simple harmonic motion when damping is present?
A 
The damping force is always in the opposite direction to the velocity. 
B 
The damping force is always in the opposite direction to the acceleration. 
C 
The presence of damping gradually reduces the maximum potential energy of the system. 
D 
The presence of damping gradually reduces the maximum kinetic energy of the system. 
Q9. 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 
Q10. 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 
0.5 s 
B 
1.0 s 
C 
1.4 s 
D 
2.0 s 
Q11. Which one of the following statements always applies to a damping force acting on a vibrating system?
A 
It is in the same direction as the acceleration. 
B 
It is in the same direction as the displacement. 
C 
It is in the opposite direction to the velocity. 
D 
It is proportional to the displacement. 
Q12. Which one of the following statements concerning the acceleration of an object moving with simple harmonic motion is correct?
A 
It is constant. 
B 
It is at a maximum when the object moves through the centre of the oscillation. 
C 
It is zero when the object moves through the centre of the oscillation. 
D 
It is zero when the object is at the extremity of the oscillation. 
Q13. When the length of a simple pendulum is decreased by 600 mm, the period of oscillation is halved. What was the original length of the pendulum?
A 
800 mm 
B 
1000 mm 
C 
1200 mm 
D 
1400 mm 
Q14. Which one of the following gives the phase difference between the particle velocity and the particle displacement in simple harmonic motion?
A 
/4 rad 
B 
/2 rad 
C 
3/4 rad 
D 
2 rad 
Q15. A body executes simple harmonic motion. Which one of the graphs, A to D, best shows the relationship between the kinetic energy, E_{k}, of the body and its distance from the centre of oscillation?
Q16. The displacement (in mm) of the vibrating cone of a large loudspeaker can be represented by the equation x = 10 cos (150t), where t is the time in s. Which line, A to D, in the table gives the amplitude and frequency of the vibrations.

amplitude/mm 
frequency/Hz 
A 
5 
10/2 
B 
10 
150 
C 
10 
150/2 
D 
20 
150/2 
Q17. A mechanical system is oscillating at resonance with a constant amplitude. Which one of the following statements is not correct?
A The applied force prevents the amplitude from becoming too large.
B The frequency of the applied force is the same as the natural frequency of oscillation of the system.
C The total energy of the system is constant.
D The amplitude of oscillations depends on the amount of damping.
Q18. A particle of mass 0.20 kg moves with simple harmonic motion of amplitude 2.0 × 10^{–2}m.
If the total energy of the particle is 4.0 × 10^{–5}J, what is the time period of the motion?
A – π/4 seconds
B – π/2 seconds
C  π seconds
D  2π seconds
Q19. The graph shows the variation in displacement with time for an object moving with simple harmonic motion.
What is the maximum acceleration of the object?
A 0.025 m s^{–2}
B 00.99 m s^{–2}
C 002.5 m s^{–2}
D 009.8 m s^{–2}
Q20. Two pendulums, P and Q, are set up alongside each other. The period of P is 1.90 s and the period of Q is 1.95 s.
How many oscillations are made by pendulum Q between two consecutive instants when P and Q move in phase with each other?
A 19
B 38
C 39
D 78
Q21. A particle of mass m oscillates in a straight line with simple harmonic motion of constant amplitude. The total energy of the particle is E.
What is the total energy of another particle of mass 2m, oscillating with simple harmonic motion of the same amplitude but double the frequency?
A 2E
B 2E
C 4E
D 8E
Q22. When a mass suspended on a spring is displaced, the system oscillates with simple harmonic motion.
Which one of the following statements regarding the energy of the system is incorrect?
A The potential energy has a minimum value when the spring is fully compressed or fully extended.
B The kinetic energy has a maximum value at the equilibrium position.
C The sum of the kinetic and potential energies at any time is constant.
D The potential energy has a maximum value when the mass is at rest.
Q23. When a mass M attached to a spring X, as shown in Figure 1, is displaced downwards and released it oscillates with time period T.
An identical spring is connected in series and the same mass M is attached, as shown in figure 2.
What is the new time period?
A T/2
B
C
D 2T