A block is attached to a spring and is placed on a horizontal smooth surface as shown in which spring is unstretched. Now the spring is given an initial compression `2x_(0)` an block is released from rest. Collision with the wall `PQ` are elastic.

Write its equation of motion indicating position as a function of time:

Options

A. `x =- 2x_(0) cos omegat 0 lt t lt (T)/(2)`
B. `x =- 2x_(0) cos (omegat +(2pi)/(3))(T)/(2) lt t lt T`
C. `x =- x_(0) cos omega t 0 lt t lt (T)/(2)`
D. `x =- 2x_(0) cos (omegat +(pi)/(3))(T)/(2) lt t lt T`

Answer

A, B

Explanation

A block is attached to a spring and is placed on a horizontal smooth surface as shown in which spring is unstretched. Now the spring is given an intial compression `2x_(0)`and block is released form rest. Collisions with the wall `PQ` are elastic.

`x=- 2x_(0)cos omegat, -0 lt t lt (T)/(2)`
`x =- 2x_(0) cos (omegat +(2pi)/(3)), (T)/(2) lt t lt T`