The displacement of a particle is given by. x = A cosωt. Which of the following graph represents variation in potential energy as a function of time t and displacement x.
(A) I,III
(B) II,IV
(C) II,III
(D) I,IV
The correct option (A) I,III
Explanation:
x = A cos ωt
PE = Potential energy = (1/2) mω2 x2
when x = 0, PE = 0
Put x = A cos ωt hence
PE = (1/2) mω2 (A cos ωt)2
= (1/2) mω2 × A2 cos2ωt
at t = 0, PE = (1/2) mω2A2
hence graph represents option I & III
