|Nov7-09, 03:27 PM||#1|
Matching Initial Position and Velocity of Oscillator
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)
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.
|Nov7-09, 03:34 PM||#2|
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)
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