Finding different variables from this oscillation...?

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?

Explain your work. Thanks! :)

Answer 1

displacement x = (6.0 ) cos [ ( 3 pi )t + pi/3 ]
velocity v=dx/dt= -18pi sin(3pit + pi/3)
acceleration a=dv/dt= -54 pi^2cos(3pit + pi/3)

x(2) = 6.0 cos [ ( 3 pi )2 + pi/3 ]=
a) x(2) =6.0 cos(19/3 pi)= 6(0.5)= 3m

b) v(2)=- 18 pi sin(6pi + pi/3) = 49.0 m
c) a(2) = -54 pi^2cos(3pi2 + pi/3)= _____
d) Phase = pi/3

e) f= 3pi/2pi= 1.5Hz
f )T=1/f= 2/3= .6667sec

:-) you are welcome.