The PE of a harmonic oscillator of mass 2 kg in its mean position is 4 J. If the total energy is 8 J and its amplitude is 0.01 m, its time period in second will be

Options

A. `(pi)/(10)`
B. `(pi)/(20)`
C. `(pi)/(50)`
D. `(pi)/(100)`

Answer

D

Explanation

Potential energy of the oscillator is
`(1)/(2) kx^(2) = 8-4 = 4J`
`rArr k = (4xx2)/(x^(2))=(8)/((0.01)^(2))`
` = 8 xx 10^(4)N//m`
`therefore T = 2pisqrt((m)/(k)) =2pisqrt((2)/(8xx10^(4)))`
` = (pi)/(100)s`