Velocity for SHM oscillator...?

Question

A body oscillates with simple harmonic motion according to the equation:

x = (6.0 m) cos [ ( 3 pi rad/s )t + pi/3 rad ]

At t = 2.0 s, what are (a) the displacement, (b) the velocity, (c) the acceleration, and (d) the phase of the motion?

Also, what are (e) the frequency and (f) the period of the motion?

What equations did you use? Can you explain your answers?

Answer 1

Your formula give the displacement, just put in the value of t. The velocity is the derivative of the displacement, Take the derivative dx/dt and put in the value of t. The acceleration is the second derivative of displacement, or the first derivative of velocity. Same method. The period is given by ∆t when the argument of cosine goes from 0 to 2π, and the frequency is 1/period.