MIT 1803 lecture 10

This lecture covered the homogeneous second order equation as it applied to the damped harmonic oscillator.  The characteristic equation was extracted, and explored a little bit.

y'' = 2py' - w_0^2y = 0

leads to

r^2 + pr + w_0^2 = 0 \quad \quad r = -p +- (p^2 -w_0^2)^{1/2}

The work done on the blackboard is so careful.  He focuses on the quality of the path to the solution, always making sure to do the least work possible, making the solution simple.  He underscores that “writing it all out” is the hack method, and it is prone to error as well.

I now see that confusion I before is mostly resolved by really understanding that

\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}

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