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Matching Initial Position and Velocity of Oscillator

by Linus Pauling
Tags: initial, matching, oscillator, position, velocity
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Linus Pauling
#1
Nov7-09, 03:27 PM
P: 190
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.
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Linus Pauling
#2
Nov7-09, 03:34 PM
P: 190
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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