Physics angular frequency, aplitude

Question

The velocity of a simple harmonic oscillator is given as v = -5.30 sin(21.5 t) (mks units).  What is its angular frequency?

What is the amplitude of the motion?

Where is the mass at 37.7 seconds?

If the mass is 0.300 kg, what is the spring’s potential energy at this moment?

What is its kinetic energy at this moment?

Answer 1

V = - AwSinwt = -5.3 Sin 21.5 t 

If X = ACoswt  = A Cos 21.5 t

where w= Angular velocity 21.5 rad/sec

As Aw = -5.3 

A = Amplitude =( 5.3 / 21.5 )m

X = A at t = 0

X = (5.3/21.5) Cos (21.5*37.7) at 37.7 sec = 0.246 Cos ( 810.55)m

Spring PE = 1/2 KX ² Where K = w ² * Mass 

PE = (1/2 ) (21.5) ² * 0.3 

KE =  Max enery - PE

Max energy = 1/2 K * (amplitude) ²