(Mass–spring system under general initial conditions)
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
(Mass–spring system under general initial conditions)
(i) Define amplitude and phase constant for the linear simple harmonic motion of a particle attached to an ideal spring. State the physical significance of each term.
(ii) A particle executing SHM has an initial displacement x0 and initial velocity v0 at t=0. Explain qualitatively, without using any numerical values, why knowledge of both x0 and v0 is sufficient to fix the amplitude and the phase constant uniquely.
(iii) Using suitable reasoning, identify the value(s) of the phase constant that correspond to the following special initial situations:
(a) the particle is released from one extreme position,
(b) the particle passes through the mean position moving in the positive x–direction,
(c) the particle is momentarily at rest at the mean position.