A particle executes SHM.
(a) What fraction of total energy is kinetic and what fraction is potential when displacement is one half of the amplitude?
(b) At what value of displacement are the kinetic and potential energies equal?

Answer

A, B, C, D

Explanation

Here, let us take minimum potential energy at mean position
` U_(0)=0`
We know that `E_(t otal) = (1)/(2)m omega^(2)A^(2)`
`KE=(1)/(2)m omega^(2)(A^(2)-x^(2))` and `U=(1)/(2)m omega^(2)x^(2)`
(a) When `x=(A)/(2)`
`KE=(1)/(2)m omega^(2)((3A^(2))/(4))`
`rArr (KE)/(E_(t otal))=(3)/(4)`
At `x=(A)/(2)`, `U=(1)/(2)m omega^(2)((A^(2))/(4))`
`rArr (PE)/(E_(t otal))=(1)/(4)`
(b) Since, `K=U`
`(1)/(2)m omega^(2)(A^(2)-x^(2))=(1)/(2)m omega^(2)x^(2)`
or `2x^(2)=A^(2)` or `x=(A)/sqrt(2)=0.707A`