Question

The energy of system in simple harmonic motion is given by $E=\frac{1}{2}m{\omega }^2{A}^2.$ Which of the following two statements is more appropriate?
(A) The energy is increased because the amplitude is increased.
(B) The amplitude is increased because the energy is increased.

Answer 1

Statement A is more appropriate because the energy of a system in simple harmonic motion is given by $E=\frac{1}{2}m{\omega }^2{A}^2.$

If the mass (m) and angular frequency (ω) are made constant, Energy (E) becomes proportional to the square of amplitude (A²).
i.e. E ∝ A²

Therefore, according to the relation, energy increases as the amplitude increases.