The equation of the simple harmonic motion of a particle is x=0.05msin1/5(39.2t+5.2). Find the amplitude, Period, frequency and the initial phase of the motion

Question

X=0.05msin1/5(39.2t+5.2)

Answer 1

Amplitude:

 

A = 0.05 m

 

 

Period:

 

omega = 1/5 * 39.2 rad/s = 7.84 rad/s

 

T = 2*pi / omega = 2*pi / 7.84 sec = 0.80 sec

 

 

Frequency:

 

f = 1/T = 1/0.80 Hz = 1.25 Hz

 

 

Initial phase:

 

Set t=0 in the argument of the sine function, so

 

phi = 1/5 * 5.2 rad = 1.04 rad