Question

For a SHM, if the maximum potential energy become double, choose the correct statements.

• A. Maximum kinetic energy will become double.
• B. The total mechanical energy will become double.
• C. Both (a) and (b)
• D. Neither (a) nor (b)

Answer 1

Answer: (C)

For a particle executing SHM, its kinetic energy,
$KE=\frac{1}{2}m{\omega }^2\left(A^2-x^2\right)$
$\Rightarrow (KE{)}_{\max }=\frac{1}{2}m{\omega }^2{A}^2$
Potential energy, $PE=(PE{)}_{\max }=\frac{1}{2}m{\omega }^2{A}^2$
Total mechanical energy $TE=KE+PE$
$=\frac{1}{2}m{\omega }^2{A}^2$
$\Rightarrow TE=(KE{)}_{\max }=(PE{)}_{\max }$
So, if maximum potential energy becomes double, then both total energy and kinetic energy will also become double.
Thus, the statements given in both options (a) and (b) are correct.