Two simple harmonic oscillators of masses m, 4m have same energy. If their amplitudes are in the ratio 1 : 2, the ratio of their periods is

Options

A. `1 : 2`
B. `1 : 4`
C. `1 : 1`
D. `2 : 1`

Answer

B

Explanation

`E=(1)/(2)momega^(2)A^(2)`
`E_(1)=E_(2)`
`m((2pi)/(T_(1)))^(2)xx(1)^(2)=4mxx((2pi)/(T_(2)))^(2)xx(2)^(2)`
`(T_(1)^(2))/(T_(2)^(2))=(1)/(16)implies(T_(1))/(T_(2))=(1)/(4)`.