Question

The kinetic energy and the potential energy of a particle executing `SHM` are equal The ratio of its displacement and amplitude will be
A. `(1)/(sqrt(2))`
B. `sqrt(3)/(2)`
C. `(1)/(2)`
D. `sqrt(2)`

Answer 1

Correct Answer - A
Given `KE = PE rArr (1)/(2) mv^(2) =(1)/(2) kx^(2)`
`rArr(1)/(2) m omega^(2)(a^(2) - x^(2)) =(1)/(2) m omega^(2)x^(2)`
`rArr a^(2) - x^(2) = x^(2) rArr x^(2) = (a^(2))/( 2) rArr (x)/(a) = (1)/(sqrt(2))`