Question

In simple harmonic motion, the total mechanical energy of the given system is $E$. If the mass of the oscillating particle $P$ is doubled, then the new energy of the system for the same amplitude is:

• A. $\frac{E}{\sqrt{2}}$
• B. E
• C. $E\sqrt{2}$
• D. $2E$

Answer 1

Answer: (B)

E

Answer 2

In a simple harmonic oscillator, the total mechanical energy (T.E.) is given by:
$T.E. = \frac{1}{2}kA^2,$ where $k$ is the spring constant and $A$ is the amplitude of oscillation.

- Since the amplitude $A$ remains the same, the total mechanical energy (T.E.) will also remain the same, as it depends only on $k$ and $A$, not on the mass $m$ of the oscillating particle.

Thus, even if the mass of $P$ is doubled, the total mechanical energy $E$ will remain unchanged.

Answer: E