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

                       = - ω² 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.