Finding general solution of motion of forced harmonic oscillator

AI Thread Summary
The motion of a forced harmonic oscillator is described by the equation d^2x/dt^2 + (w^2)x = 2cos t, with specific solutions depending on whether w equals 2 or not. For w = 2, the general solution involves resonance, leading to a particular solution that includes a term proportional to t. When w is not equal to 2, the solution can be found using the method of undetermined coefficients, yielding a sinusoidal response without resonance effects. The discussion emphasizes starting with the free harmonic oscillator solution d^2x/dt^2 + (w^2)x = 0 to understand the system's behavior. Overall, solving the forced oscillator requires careful consideration of the system's parameters and the form of the forcing function.
Redgal
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1. The motion of a forced harmonic oscillator is determined by
d^2x/dt^2 + (w^2)x = 2cos t.
Determine the general solution in the two cases w = 2 and w is not equal to 2.

To be honest I've no idea where to start!
 
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Can you solve the equation for a free harmonic oscillator?
d^2x/dt^2 + (w^2)x = 0

Can you guess the general shape of a solution for the forced oscillator? You can use this as ansatz for your equation, and solve it to get the coefficients.
 
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