A particle executing simple harmonic motion is described by
MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
A particle executing simple harmonic motion is described by x=Acos(ωt+ϕ). Answer the following questions related to the idea of phase:
(i) What is meant by the phase of the motion? Distinguish between initial phase and phase at a later time t.
(ii) Two identical oscillators have the same amplitude and angular frequency but differ in initial phase by π/2. Explain, with reasons, whether they cross the mean position simultaneously after the start of observation.
(iii) Show that for any two oscillators of identical angular frequency ω, the phase difference Δϕ at an instant equals ωΔt, where Δt is the difference in time taken by them to attain the same phase value.