Question

A particle starts from the extreme position, at t = 0, in a SHM. If the time period of motion is 2s & maximum speed is 5m/s, find the equation of motion.

(a) x = 1.59cos(πt)

(b) x = 1.59sin(πt)

(c) x = 2.5sin(2t)

(d) x = 2.5cos(2t)

This question was addressed to me in final exam.

I would like to ask this question from Simple Harmonic Motion in section Oscillations of Physics – Class 11

Answer 1

Correct answer is (a) x = 1.59cos(πt)

Easiest explanation: T = 2s. ∴ w = 2π/T =  s^-1.                                                                                                                                            Aw = 5. ∴ A = 5/π metre.                                                                                                                                                                                                                                 x = 5/π sin(πt + a), where is phase constant.                                                                                                                     At t = 0, x = A. Thus, a = π/2.                                                                                                                                                                   x = 5/π sin(πt + π/2)                                                                                                                                                                            = 5/π cos(πt) = 1.59cos(πt).