The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The maximum speed of junction P is `V_0`. Assume springs are massless. Select the correct option/s

Options

A. Amplitude of potential energy is springs `S_(1)` and `S_(2)` is respectivley `1/9 kA^(2)` and `kA^(2)`
B. Amplitude of potential energy is `S_(1)` and `S_(2)` is respectively `2/9 kA^(2)` and `1/9 kA^(2)`
C. `V_(0)=Asqrt((8k)/(27 M))`
D. `V_(0)=Asqrt((8k)/(81M))`

Answer

BC

Explanation

`(2k)/3 A =kS_(p)`
`Sp_(1)=2/3 A`
`Sp_(2)=A/3`
`U_("1 max") =1/2 k xx(4A^(2))/9=(2kA^(2))/9`
`U_("2 max")=1/2 2 k xx(A^(2))/9=(kA^(2))/9`
`V_(0)=(2A)/3xxsqrt((2k)/(3m))`