A block of mass `m` connected to a spring of stiffness `k` is placed on horizontal smooth surface. When block is at `x=0`, spring is in natural length. The block is also subjected to a force `F=(k|x|)/(@)` then

Options

A. Motion of block is SHM
B. Time period of motion is `pisqrt((m)/(k))[sqrt(2)+sqrt((2)/(3))]`
C. Time period of motion is `pisqrt((m)/(k))[1+sqrt((3)/(2))]`
D. Sum of potential energy and kinetic energy of spring block system is maximum at right extreme.

Answer

B, D

Explanation

`k_(eq)=(k)/(2)` for displacement to right `impliesT_(1)=pisqrt((2m)/(k))`
`k_(eq)=(3k)/(2)`, for displacement `impliesT_(2)=`
`pisqrt((2m)/(3k))`
`implies` motion is not `SHM`
Time period `T=T_(1)+T_(2)`
Work done by F is maximum when block reaches the right extreme