SHM problem

30.) x0 = displacement of m

let amplitude of M=x

m(x0-x) - Mx = 0 = com at rest initially

=> x = mx0/(m+M) ----------> amplitude of M

amplitude of m = Mx0/(m+M)

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now vel of m= Mv0/(m+M)

vel of M= mv0/(m+M)

extension in spring = x0

now... by energy method..

U= 1/2M[mv0/(m+M)]² + 1/2m[ Mv0/(m+M)]² + 1/2kx0²

now differentiate and do al the traditional works ;)

then u will get

T= 2pi√μ/k

where μ=mM/M+m