Question

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

Options

• acceleration

• total energy

• displacement

• velocity

Answer 1

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

Explanation:

For a particle executing simple harmonic motion (SHM),

Total energy = kinetic energy + potential energy

`= "E"_"K" + "E"_"P" = 1/2 "mv"^2 + 1/2 "kx"^2`

`= 1/"m"("A"^2 - x^2) + 1/2"m"omega^2"A"^2  ....(because "v" = sqrt("A"^2 - x^2) "where, A is the amplitude of the particle")`

`= 1/2 "KA"^2`

t 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(ωt + Φ)

(where, A = amplitude, w =angular velocity t = time, Φ = initial phase of the particle)

i.e., displacement varies periodically with time t.

Velocity of particles executing SHM,

v = `"dx"/"dt" = omega sqrt("A"^2 - x^2)`

which varies with x.

Acceleration of the particle,

a = `"dv"/"dt" = - omega^2x`

Which also varies with x.