Question

The total mechanical energy of a spring-mass system in simple harmonic motion is $E=\frac{1}{2} m \omega^{2} A^{2}$. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude $A$ remains the same. The new mechanical energy will

• A. become $2E$
• B. become $E / 2$
• C. become $\sqrt{2} E$
• D. remain $E$

Answer 1

Answer: (D)

$E=\frac{1}{2} m \omega^{2} A^{2}=\frac{1}{2} m\left(\sqrt{\frac{k}{m}}\right)^{2} A^{2}$
$\Rightarrow E=\frac{1}{2} k A^{2}$
Total energy depends on $k$ of spring and amplitude $A$. It is independent of mass