Question

The oscillator has energy of oscillations E. If the mass of oscillator is doubled the energy now for same oscillation amplitude becomes

• A. E / 2
• B. E / 4
• C. E
• D. 2 E

Answer 1

Answer: (C)

E

Energy of oscillator 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 $E=\frac{1}{2}m\times \frac{K}{m}\times A^2$

$⟹E=\frac{1}{2}K{A}^2$ which states that energy is independent of mass of the oscillator.

Thus for same oscillation amplitude, energy of oscillator will remain the same.