First slide

Simple harmonic motion

Question

Energy of a spring-mass oscillator increases if

Easy

A

its mass is increased keeping the amplitude same
B

its amplitude is increased but mass is decreased
C

its speed at the mean position is increased
D

Both (2) and (3)

Solution

$T = 2 π \sqrt{\frac{m}{K}}$ and $K = m ω^{2}$ for a spring-mass system. Total mechanical energy = $\frac{1}{2} K A^{2}$ .
For (A): Since, energy depends on K, A, changing mass does not change energy.
For (B): Same explanation as for (A).
For (C): Maximum kinetic energy (which is at mean position) = Total mechanical energy = $\frac{1}{2} K A^{2}$
It is independent of mass, only depends on K of spring, and amplitude of motion.

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