Question

A particle executes S.H.M. having time period T, then the time period with which the potential energy changes is(a) T(b) 2T(c) T/2(d) ∞

Answer 1

standard equation of motion of particle in SHM is given by, $x=Asin\left(\frac{2\pi}{T}\right)$

where A is amplitude and T is time period.

and also we know, potential energy is given by, $P.E=\frac{1}{2}kx^2$

hence, potential energy depends upon displacement of particle.

we know, sine function changes zero to maximum twice in its period (2π) so, potential energy changes zero to maximum twice in its period

hence, potential energy changes zero to maximum twice in each vibrations so its time period is T/2

hence, option (c) is correct