Solve - 

A system consists of a cart having mass M and a block of mass m , attached to a spring of a constant k.The block is kept on the cart . Initially , the cart and the block are at rest and the spring is streched through a distance x , when the system is released . Find the time periods of the two SHM's and the amplitudes of the SHM of the block and of the cart as seen from the road .

For figure , pls consult HC verma , Ch- SHM , pg-254 , que -30 (acc. to my book )

first try to solve ques.49 page 163 of ur hcv book

definitely u will be able to solve it

Let mass M be stretched by x₁ and m by x_2.

x₁ +x₂ =x

 

and Mx₁=mx₂

hence,

x₁=mx/M+m

x₂=Mx/M+m

 

now On mass M,

F=kx

 =k*(M+m)*x₁/m

as we get F is drectly proportional to x₁, we can write

  k*(M+m)*x₁/m=Mw²x₁

  therefore, w=