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Sunday, November 21, 2010

Watched MIT 18.03 - lecture 14

In this lecture we hear that Prof. Mattuck plays the cello. Yet another example of a mathematician with a love ( or talent ) for classical music. To the math.

This lecture is about the following differential equation that represents a system with a resonance frequency $\omega$ and the input to the system with frequency $\omega_1.$

$y'' + \omega^2y = \cos{(\omega_1x)}$

If $\omega_1 \neq \omega$ then the solution is: $y=C1\cos(\omega x)+C2\sin(\omega x)+\frac{\cos(\omega_1 x)}{\omega^2-\omega_1^2}$

If $\omega_1 = \omega$ then the solution is $y=C1\cos(\omega x)+C2\sin(\omega x)+\frac{x\sin(\omega x)}{2\omega }$

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