Matching Initial Position and Velocity of Oscillator

[Linus Pauling]

1. Find C and S in terms of the initial position and velocity of the oscillator.
Give your answers in terms of x_0, v_0, and omega. Separate your answers with a comma.



2. x(t) = X_0 + v_0*t + 0.5at^2
x(t) = C*cos(omega*t) + S*sin(omega*t)



3. Taking the derivative of x(t):

v(t) = -C*omega*sin(omega*t) + S*omega*sin(omega*t)

Thus,

x_0 = C
v_0 = S*omega

How don't quite see how to solve for C and S in terms of x_0, v_0, and omega only.

 

[Linus Pauling]

This is as good as I've gotten it:

C = [x_0 + v_0*t + 0.5at^2] / cos(omega*t)

S = [x_0(1-cos(omega*t)) + v_0*t + 0.5at^2] / sin(omega*t)