Question

A particle executes SHM along x axis is displacement varies with time according to equation X(t)=5.4cos(6πt+π/4), where X(t) is in metres and T in seconds determine amplitude, frequency, period and intial phase​.

Answer 1

We have an SHM given by,
$x = y \cos(2\pi \: ft + a )$

y = amplitude,
x = displacement along x
f = Frequency,
t = time taken for motion,
a = phase

Comparing the given equation and this general form,
We have,

Amplitude = 5.4 m

Frequency = 3 Hz

Period = 1/frequency= 1/3 s

Inital phase = π/4