Question

The graph below shows the variation of potential energy $U(t)$, kinetic energy $K(t)$ with time $t$ for a particle executing SHM. Choose the correct statement(s).

• A. The time periods of variation of potential and kinetic energies are same.
• B. The total mechanical energy is maximum at $t=T/2$.
• C. Kinetic energy is negative and potential energy is positive.
• D. Potential energy is negative and kinetic energy is positive.

Answer 1

Answer: (A)

Kinetic energy and potential energy of a particle executing SHM are periodic with period $\frac{T}{2}$.
Time periods of variation of potential and kinetic energies are same.
However, for such a particle the total mechanical energy, i.e. $U(t)+K(t)$ remains constant always.
This can also be seen from the graph given in question.
Also, kinetic and potential both energies are positive. Thus, statement given in option (a) is correct, rest are incorrect.