Question

A harmonic motion is given by x(t)=30sin(50t−π/3)mm. where t is in second and phase angle is in radian. What will be the time period of motion?

Answer 1

Answer :

• y=0.3sin20π(t+0.05)
• y=0.3sin(20πt+π)

Comparing the given equation with the standard equation y=Asin(ωt+ϕ)

By comparison

ω=20π

⇒phi=π

⇒A=0.3

Thus, amplitude and initial phase is known

Amplitude (A)=0.3m

Initial phase (ϕ)=π

Then, for calculating time period

T= ω2π = 202π = 101

s=0.1s

⇒ Time period (T)=0.1s

Also for initial displacement t=0

⇒y=0.3sin(π)=0

Thus, initial displacement =0.