Question

The particle executing simple harmonic motion has a kinetic energy of $K_0{\cos }^2\omega t$. The maximum values of the potential energy and the total energy are respectively

• A. $K_0$ and $K_0$
• B. $0$ and $2K_0$
• C. $\frac{K_0}{2}$ and $K_0$
• D. $K_0$ and $2K_0$

Answer 1

The correct option is A $K_0$ and $K_0$

The kinetic energy of particle executing S.H.M is $K.E=K_0{\cos }^2\omega t$

Maximum value $K.E$ is $K.E_{mean}=K_0$

Now, the total energy of S.H.M is same as the maximum value of $K.E$, which is $K_0$

Similarly the maximum value of potential energy of S.H.M is same as the maximum value of $K.E$, which is $K_0$