Question

The displacement of a particle in a periodic motion is given by `y = 4cos^2(t/2)sin(1000t)`. This displacement may be considered the result of the superposition of n independent harmonic oscillation. Find the value of n.

Options

• 1

• 2

• 3

• 4

Answer 1

3

Explanation:

Given, `y = 4cos^2(t/2)sin(1000t)`

= `2 xx 2cos^2(t/2)sin(1000t)`

= 2(1 + cost) sin(1000t)        ..........(∵ 2cos²θ = 1 + cosθ)

= 2sin(1000t) + 2cost.sin(1000t)

= 2sin(1000t) + sin(1000t + t) + sin(1000t - t)

= 2sin(1000t) + sin(1001t) + sin(999)t

So, n = 3      ............(∵ The above equation shows three independent oscillations passed with each other.)