19.1 Characteristics of Simple Harmonic Motion

1.            Which of the following statements is true regarding a simple harmonic motion?

• Frequency increases with time

• Acceleration does not change with time

• Displacement from the equilibrium position is small

• Frequency increases with time

Answer explanation

D

2. The graph shows the variation of displacement with time for two particles performing simple harmonic motion with the same frequency and amplitude. What is the phase difference between the two motions?

Answer explanation

                     

                    

                          

3. 3. Which of the following statements is true about a body performing simple harmonic motion in a straight line between X and Y?

• The speed is minimum at the midpoint of XY.

• The total energy is maximum at X and Y.

• The magnitude of the restoring force is maximum at X and Y.

• The magnitude of linear momentum is maximum at X and Y.

Answer explanation

·      At X and Y, the displacement is maximum (amplitude).

·      Thus, the acceleration is also maximum

·      Therefore, the restoring force is maximum

4. 4. The graph below shows the variation of acceleration a with displacement x of a particle performing a simple harmonic motion. The frequency of oscillation of the simple harmonic motion is

• 0.87 Hz

• 1.15 Hz

• 4.77 Hz

• 34.41 Hz

Answer explanation

5. 5. A particle performs an oscillation without damping. Which of the following quantities is not constant for the oscillation?

• Force

• Amplitude

• Total energy

• Angular frequency

6. 6. Which of the following statements about an object which performs simple harmonic motion is true?

• The acceleration is maximum when the velocity is maximum.

• The acceleration is maximum when the displacement is maximum.

• The maximum potential energy is greater than the maximum kinetic energy.

• The maximum kinetic energy is greater than the maximum potential energy.

Answer explanation

In simple harmonic motion, acceleration is directly proportional to the displacement.

7. 7. Which is not true of a simple harmonic motion?

• It is a periodic motion.

• Its motion involves a restoring force.

• The potential energy is always the same with its kinetic energy.

• The total energy of the motion is conserved.

Answer explanation

In simple harmonic motion, the potential energy is same to the kinetic energy only at two positions, and not at all positions or at all time

8. 8. An object of mass m undergoes a simple harmonic motion with frequency f and amplitude A. The maximum restoring force is

Answer explanation

• The value of k does not depend on y.

• The period of the motion depends on y.

• The velocity of the particle is directly proportional to y.

• The acceleration of the particle is always directed away from the equilibrium point.

Answer explanation

10. 10. The table shows the position x at the corresponding time t for a particle that performs simple harmonic motion along a straight line. If the position  is the centre of the oscillation of the particle, the period of the motion is

• 4 s

•  8 s

• 12 s

• 16 s

Answer explanation