Question

Which of the following statements are correct?
A. All oscillatory motion is Simple Harmonic Motion.
B. Simple Harmonic motion is a special case of oscillatory motion.
C. Oscillatory motion is a special case of Simple Harmonic motion.
D. Oscillatory motion cannot be Simple Harmonic motion

Which of the following statements is correct?
A. In simple harmonic motion, kinetic energy is constant.
B. In simple harmonic motion, potential energy is constant.
C. In simple harmonic motion, the sum of kinetic and potential energy is constant.
D. In simple harmonic motion, the difference between kinetic and potential energy is constant.

Answer 1

Which of the following statements are correct?

Correct Option: B. Simple Harmonic motion is a special case of oscillatory motion.

Oscillatory motion is a general term for any motion that repeats over time. For example: heart beat.

The simple harmonic motion (SHM) is a special case of oscillatory motion. SHM is repetitive but the repetitive motion is such that the restoring force is proportional to the displacement from the mean position. It is always sinusoidal.

The example of SHM is oscillation of spring-mass system. The restoring force of a spring satisfies Hooke's law, that is, restoring force is directly proportional to the displacement from its natural length.

Incorrect: A. All oscillatory motion is Simple Harmonic Motion.

Not all oscillatory motion is SHM for example heart beat.

Incorrect: C. Oscillatory motion is a special case of Simple Harmonic motion.

Oscillatory motion is a more general term and SHM is a special case of oscillatory motion.

Incorrect: D. Oscillatory motion cannot be Simple Harmonic motion

Since SHM is repetitive motion, oscillatory motion can be SHM.

Which of the following statements is correct?

Correct Option: C. In simple harmonic motion, the sum of kinetic and potential energy is constant.

In simple harmonic motion, the motion is fastest at the mean position and the system is motionless at the extreme positions. For example in spring-mass system, the mass is at rest when it is at the farthest distance from the mean position, and the mass move at the fastest speed while passing through the mean position. Kinetic energy is 0.5mv² is proportional to square of speed, so kinetic energy of the mass is greatest at the mean position and zero at the extreme positions. So, kinetic energy is not constant.

The potential energy of spring U=0.5kx² is proportional to the square of the displacement of the spring. It is zero when x=0, that is at the mean position. And highest at the extreme position. So, potential energy is also not constant in SHM.

The total energy of the system is the sum of the kinetic and the potential energy. By the conservation of energy, the total energy is conserved.