Consider the situation in which one end of a massless spring of spring constant k is connected to a cylinder of mass m and the other to a rigid support. When cylinder is given a gentle push in horizontal direction it starts oscillating on the rough horizontal surface. During the oscillation cylinder rolls without slipping. When calculated, motion of cylinder is found to be S.H.M. with time period `T=2pisqrt((3m)/(2K))` and equation of SHM is `x=Asinomegat`, where symbols have their usual meaning.

At a distance `x_(1)` from the equilibrium position, kinetic energy of the oscillating system becomes equal to potential energy then, `x_(1)`is equal to:
Q The equation which correctly shows the variation in friction as a function of time is-

Options

A. `(KA)/(3)sinomegat`
B. `Asinomegat`
C. `(3)/(2)Kacosomegat`
D. `Acosomegat`

Answer

A

Explanation

`kx_(1)-f=mw^(2)x_(1)`
`f=kx_(1)-mw^(2)x_(1)`
=`(k-(m)((2k)/(3m)))x_(1)=(k)/(3)x_(1)=(k)/(3)Asinomegat`
`f=(kA)/(3)sinwt`