Question

The displacement of a particle from its mean position is given by x = 4 sin (10πt + 1.5π) cos (10πt + 1.5π). The motion of the particle is

विकल्प

• Simple harmonic motion with period 10πs

• Non-periodic

• Simple harmonic motion with period 0.1s

• Simple harmonic motion with period 0.2s

Answer 1

Simple harmonic motion with period 0.1s

Explanation:

Given Y = 4 sin (10πt + 1.5π) cos (10πt + 1.5π) 

from 2 sin A cos A = sin 2A

Y = 2 sin2 (10πt + 1.5π)  = 2 sin (20πt + 3π) 

Now comparing witj equation Y = a sin (ωt + Φ)

we get ω = 20π 

∴ Time Period T = `(2π)/ω = (2π)/(20π) = 0.1` second