The quantity which does not vary periodically for a particle performing SHM is

Options

A. acceleration
B. total energy
C. displacement
D. velocity

Answer

B

Explanation

For a particle executing simple harmonic motion (SHM),
Total energy = kinetic energy + potential energy
`=E_(K)+E_(P)=1/2mv^(2)+1/2kx^(2)`
`=1/m(A^(2)-x^(2))+1/2momega^(2)A^(2)`
`(becausev=sqrt(A^(2)-x^(2))` where, A is the amplitude of the particle`)`
`=1/2KA^(2)`
It is independent oft, xis remains constant i.e., it does not vary periodically.
However, the displacement of a particle executing SHM along x-axis is given by
`x=Asin(omegat+phi)`
(where, A= amplitude, `omega` = angular velocity t = time, `phi` = initial phase of the particle)
i.e., displacement varies periodically with time t.
Velocity of particles executing SHM,
`v=(dx)/(dt)=omegasqrt(A^(2)-x^(2))`
which varies with x.
Acceleration of the particle,
`a=(dv)/(dt)=-omega^(2)x`
Which also varies with x.