Question

Differentiate the following equation with respect to t and explain it ?
Its equation of Simple Harmonic Motion.

Answer 1

x = A sin(omega*t + phi)
Here,
A = Amplitude of the simple harmonic motion

Omega is the angular frequency of the SHM in motion.
phi is the initial phase angle here,
Now we've been told to differentiate it with respect to Time.


This means,
d(x)/dt = d(A sin(omega*t + phi)/dt
dx / dt will give us the velocity(v) of the particle in simple harmonic motion.

Therefore,
v = A cos(omega*t + phi) * d(omega*t + phi)/dt because of chain rule.

Therefore,
Velocity = A * cos(omega*t +phi) * omega

Therefore,
Final equation will be
Velocity = A*omega * cos(omega*t +phi)

Here, we've used the chain rule as well as the rule of differentiation of trig functions that is the differentiation of sin function in this case.

{ d(sinx)/dx } = cos x