Compute amplitude and frequency of the particle:
The displacement of a particle is described by x = 5 + 3 cos 3 t. Determine the position of the particle at t = 3 seconds. Compute amplitude and frequency of the particle.
Solution
x = 5 + 3 cos (3t )
at t = 3 x = 5 + 3 cos 9
= 7.96 cm.
We have
x = 5 + 3 cos 3t
∴ x - 5 = 3 cos 3t
dx /dt=- 9 sin 3t dt
d ^{2} x/ dt ^{2} =- 27 cos 3t
= - ω^{2} x
∴ ω = 3.29 rad / sec
Amplitude shall be calculated as the displacement when t = 0
∴ x = 5 + 3 cos 0^{o} = 8.
∴ Amplitude = 8 cm.