d^2x/dt^2 + w^2_0x = acos(wt)
where x is the position. Given that at t=0 we have x=dx/dt=0, find the function x(t). Use BOTH with variation of the parameters and guessing methods. Describe the solution if w is approximately, but not exactly, equal to w_0. Give an example of a physical system where this happens.© BrainMass Inc. brainmass.com December 15, 2020, 9:27 pm ad1c9bdddf
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The equation is:
The general solution is given by:
Where is the solution of the associated homogenous equation
and is a particular solution to equation (1.1).
This equation is a second order linear equation with constant coefficients.
To solve equation (1.3) we "guess" a solution in the form:
Plugging it in the homogenous solution we get:
Thus the two homogenous solutions are:
Since we are interested in real solutions, and the homogenous solution is a linear combination of these two linearly solutions, we can use Euler's identity
To express the two ...
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