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

The correct option is D remain $E$

Energy of spring-mass system is given by $E=\frac{1}{2}m{w}^2{A}^2$

Time period of the oscillation $T=2\pi \sqrt{\frac{m}{K}}$

$\frac{T}{2\pi }=\sqrt{\frac{m}{K}}⟹w=\sqrt{\frac{K}{m}}$

Thus $E=\frac{1}{2}m\times \frac{K}{m}\times A^2$

$⟹E=\frac{1}{2}K{A}^2$

Hence new mechanical energy will remain the same. i.e $E^{\prime }=E$ as energy independent of mass.