A Cyberphysics Page

Simple Harmonic Motion - Multiple Choice Questions

Q21. A particle of mass m oscillates in a straight line with simple harmonic motion of constant amplitude. The total energy of the particle is E.

What is the total energy of another particle of mass 2m, oscillating with simple harmonic motion of the same amplitude but double the frequency?

A 2E

B 2E

C 4E

D 8E

Total energy = maximum KE = maximum PE

KE_max =¹/₂ mv_max²

KE_max = 0.5 x m (2πfA)²

KE_maxis ∝to mf²

therefore the new particle will have energy x 2 (for mass doubling) and x 2² (for frequency doubling)

a multiplication factor of 2 x 4 = 8

∴ the answer is choice D