Question

A particle executes S.H.M. with a period 8s. Find the time in which half the total energy is potential. (Ans : 1 s)

Answer 1

please find the answer

Answer 2

If particle execute simple harmonic motion, equation of motion of particle is $x=Asin\omega t$

potential energy, P.E = F.dx
= 1/2m$\omega^2x^2$
And total energy, T.E = 1/2 m$\omega^2$A²

Now, A/C to question,
P.E = 1/2(T.E)
1/2m$\omega^2x^2$ = 1/2(1/2 m$\omega^2$A²)
x = A/√2

Now, $x = Asin\omega t$
A/√2 = Asin$\omega$t
$\omega t$ = π/4
so, 2π/T × t = π/4
Given, T = 8 sec
then, 2π/8 × t = π/4
t = 1 sec