Question

For a partcle executing S.H.M., the kinetic energy $K$ is given by $K=K_0{\cos }^2\omega t$. The maximum value of potential energy is:

• A. $K_0$
• B. $\frac{K_0}{2}$
• C. Not obtainable
• D. Zero

Answer 1

The correct option is A $K_0$

Given, in simple harmonic motion, the kinatic energy,
$K=K_0{\cos }^2\omega t$

If the kinetic energy is zero, the potential energy will be maximum and vice-versa,

Since total energy of the system will remain conserve
$P{E}_{max}=K{E}_{max}$

$\Rightarrow P{E}_{max}=K_0\left({\cos }^2\omega t\right)max$

$\Rightarrow P{E}_{max}=K_0\times 1$

$\Rightarrow P{E}_{max}=K_0$