Question

A point mass oscillates along the X-axis according to the relation x = x₀ cos(ωt -  π / 4). If acceleration of the particle is written as a = a₀ cos(ωt + δ ), then

(a) a₀ = x₀ω²,  δ = - π/4

(b) a₀ = x₀ω²,  δ = π/4

(c) a₀ = x₀ω²,  δ = - 3π/4

(d) a₀ = x₀ω²,  δ = 3π/4.

Answer 1

Answer is (d) a₀ = x₀ω², δ = 3π/4.

x = x₀ cos(ωt - π/4)

Comparing it with given equation,

a = a₀ cos(ωt + δ)

\(\Rightarrow\) a₀ = x₀ω² and δ = \(\frac{3\pi}{4}\)