Find the natural frequency of the system shown in figure. The pulleys are smooth and massless.

Options

A. `1/(pi)sqrt((2k)/M)`
B. `2/(pi)sqrt((2k)/M)`
C. `1/(pi)sqrt(k/M)`
D. `1/(pi)sqrt((4k)/M)`

Explanation

If the mass M is dissipated by x from its mean position each spring further stretched by 2x

Net restoring force
F=-8kx
M.a=-8kx
`f=1/(2pi)sqrt(|a/x|)=1/(2pi)sqrt((8k)/M)=1/(pi)sqrt((2k)/M)`