Matching Initial Position and Velocity of Oscillatorby Linus Pauling Tags: initial, matching, oscillator, position, velocity 

#1
Nov709, 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. 



#2
Nov709, 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(1cos(omega*t)) + v_0*t + 0.5at^2] / sin(omega*t) 


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