Question

The quantity which does not vary periodically for a particle performing S.H.M. is?
A. Acceleration
B. Total energy
C. Velocity
D. Displacement

Answer 1

Simple harmonic motion (abbreviated SHM) is a form of periodic motion in mechanics and physics in which the restoring force on a moving item is directly proportional to the size of the item's displacement and operates towards the item's equilibrium position.

Complete step-by-step solution:
Simple harmonic motion may be used to mimic a number of movements, but it is best shown by the oscillation of a mass on a spring when it is subjected to Hooke's law's linear elastic restoring force. The motion has a single resonance frequency and is sinusoidal in time. Other phenomena, such as the motion of a simple pendulum, may be described using basic harmonic motion, albeit the net force on the item at the end of the pendulum must be proportional to the displacement for it to be an accurate model. Molecular vibration can also be modelled using simple harmonic motion. The energy oscillates between the kinetic energy of the mass $K = \dfrac{1}{2}m{v^2}$and the potential energy $U = \dfrac{1}{2}k{x^2}$ stored in the spring in a basic harmonic oscillator. Because there are no dissipative forces in the mass and spring system, the total energy is equal to the sum of the potential and kinetic energy. Kinetic energy varies with velocity, and potential energy varies with location, but the total of the two remains constant.
Simple harmonic motion serves as a foundation for analysing more intricate periodic motion using Fourier analysis techniques.
Hence option b is correct.
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