The position function x (6.0 m) cos[(3p rad/s)t p/3 rad]gives the simple harmonic motionof a body. at t 2.0 s, what are the(a) displacement, (b) velocity, (c)acceleration, and (d) phase of the motion? also, what are the (e)frequency and (f) period of the motion?

The correct formula for this simple harmonic motion is:

x = (6.0) cos [ (3 pi) t + pi/3 ] 

A. Calculating for displacement x at t = 2:

x =6.0 cos (19/3 pi)
x = 6 (0.5)

x = 3 m

B. Velocity is equivalent to the 1st derivative of the equation. v = dx / dt

 Velocity v = dx/dt = -18 pi sin (3pi t + pi/3) 

v = - 18 pi sin (6pi + pi/3)

v = 49.0 m/s

C. Acceleration is the 2nd derivative or the 1st derivative of velocity dv / dt
Acceleration a = dv/dt = -54 pi^2 cos(3pi t + pi/3) 

a = -54 pi^2 cos(3pi * 2 + pi/3)

a = 386.34 m/s^2

D. Phase = pi/3 

E. frequency f= 3pi/2pi = 1.5Hz 

F. period = 1/f = 1/1.5 = .6667sec 

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