A particle is undergoing SHM. If its potential energy is given by: U = kx^2. What will be the value of x for potential energy to be 1/3rd of kinetic energy? Assume k is force constant.

A particle is undergoing SHM. If its potential energy is given by: U = kx^2. What will be the value of x for potential energy to be 1/3rd of kinetic energy? Assume k is force constant.

(a) A/√7

(b) A/√6

(c) A/√3

(d) A/√2

by (555 points)

The correct option is (a) A/√7

Explanation: Let x = Asin(wt).

U = kA^2sin^2(wt)                                                                                                                                                                       K = 1/2mA^2w^2cos^2(wt).                                                                                                                                                      Given: U = 1/3K.                                                                                                                                                                                 kA^2sin^2(wt) = (1/3)*(1/2)mA^2w^2cos^2(wt),

and k = mw^2.

∴ tan^2(wt) = 1/6. Or tan(wt) = 1/√6.

∴ sin(wt) = 1/√7.                                                                                                                                                                               x = Asin(wt) = A/√7.