Question

The displacement equation of SHM is y = 0.5 (sin 3πt + √3 cot 3πt). Find Amplitude, Angular frequency, Period of oscillation, velocity and acceleration.

Answer 1

y = 0.5 (sin 3πt + √3 cot 3πt)

y = 0.5 x 2 ( \(\cfrac12\) sin 3πt + \(\cfrac{\sqrt3}2\) cot 3πt)

y = 1 ( cot \(\cfrac{\pi}3\) sin 3πt - sin \(\cfrac{\pi}3\) cot 3πt)

y = sin( 3πt + \(\cfrac{\pi}3\))

Comparing equation

y = A sin (ωt + θ)

Then amplitude A = 1

Angular frequency ω = 3π rad/sec

Time period T = \(\cfrac{2\pi}ω\)

T = \(\cfrac{2\pi}{3\pi}\)

T = \(\cfrac23\) sec

Acceleration a = Aω²

= 1 x (3π)²

a = 9π² m/s²

Velocity v = Aω

v = 1 x 3π

v = 3π m/s