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Unformatted text preview: x plus the function itself (times a constant) is equal to zero. Thus the second derivative of our function must have the same form as the function itself. What readily comes to mind is the sine and cosine function. Let us come up with a trial solution to our differential equation, and see if it works. As a tentative solution, we write: x = a cos( bt ) where a and b are constants. Differentiating this equation, we see that =  ab sin( bt ) and =  ab 2 cos( bt ) Plugging this into our original differential equation, we see that:  ab 2 cos( bt ) + a cos( bt ) = 0 It is clear that, if b 2 = , then the equation is satisfied. Thus the equation governing simple harmonic oscillation is: simple x = a cos t...
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 Fall '10
 DavidJudd
 Physics, Acceleration, Force, Simple Harmonic Motion

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