A particle is moving in a straight line with SHM of amplitude r . At a distance s from the mean position of motino, the particle receives a blow in the direction of motion which instataneously triple the velocity. Find the new amplitude.

Explanation

Velocity, `V=omegasqrt(r^(2)-y^(2))`
At `y=s, V=V_(0),`
Due to blow, the new velocity at, `y=s` is,
`V=3V_(0),r=r^(')`
so `(3V_(0)^(2)=omega^(2)(r^(')^(2)-s^(2))` …(ii)
Dividing (ii) by (i), we have
`9=(r^(')^(2)-s^(2))/(r^(2)-s^(2))`
On solving, `r^(')=sqrt(9r^(2)-8s^(2))`