A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic en

Question

A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic energies at the displacement

Professor PC Thomas Classes · Answer

(c) : Let the displacement of particle be $x$.\ Given, Kinetic energy = Potential energy $$ \begin{aligned} & \frac{1}{2} K\left(A^2-x^2ight)=\frac{1}{2} K x^2 \ & 	ext { or } \quad A^2-x^2=x^2 \ & 	ext { or } \quad A^2=2 x^2 \ & \Rightarrow \quad x=\frac{A}{\sqrt{2}} \end{aligned} $$