Question

A body is executing SHM under the action of force whose maximum magnitude is $50N$. Find the magnitude of force acting on the particle at the time when its energy is half kinetic and half potential.

Answer 1

Force is maximum when the body is at extreme position.

Energy is half KE and half PE means, $PE=half$ $TE$ ie total energy.

$\frac{1}{2}k{A}^2=PE=TE$ when body is at extreme.

$\therefore F_{max}=50=kA$

$\therefore TE=\frac{1}{2}\times 50\times A=25A$

At the point time, $PE=KE=12.5A$

$\frac{1}{2}k{x}^2=\frac{1}{2}k(A^2-x^2)$

$A=2$