Question

The displacement for a particle performing S.H.M. is given by x = Acos(ωt + θ). If the initial position of the particle is 1cm and its initial velocity is πcms^–1, then what will be its initial phase? The angular frequency of the particle is πs^–1. 

(A) (2π/4) 

(B) (7π/4) 

(C) (5π/4) 

(D) (3π/4)

Answer 1

The correct option (D) (3π/4)

Explanation:

x = A cos (ωt + θ) (1)

V = (dx/dt) = – Aω sin(ωt + θ)  (2)

given:

when t = 0, x = 1

t = 0, v = π

ω = π

∴ from (1) & (2)

1 = A cos θ  (3)

π = – A π sin θ

i.e. 1 = – A sinθ (4)

from (3) & (4)

1 = – tanθ

tan θ  = – 1

∴ ɸ = (3π/4), (7π/4) -----

hence initial phase is (3π/4)