Notes on the underdamped harmonic oscillator damped_oscillator.ppt

## The damped harmonic oscillator

• The damped harmonic oscillator is an extension of the previous discussion by the addition of another force term to model damping.
• Clearly identify “the forces”, the restoring force, $F\left( x \right)=-m\omega _{0}^{2}x$ and and the damping force, $F_{d}\left( x \right)=-b \dot{x}$. Set the sum equal to the acceleration, $a=\frac{d^{2}x}{dt^{2}}$. (Check that the $\dot{x}$ notation is familiar).
• Discuss other types of damping forces briefly. Also metion overdamped and critically damped cases, but focus on underdamped case.
• Solve the differential equation postulating a solution $Ce^{pt}$, and obtain a solution in the “C-form” with $e^{\pm i\left( \omega _{0}+i\beta \right)t}$ terms. Find exponential damping, discuss limits etc.
• Class discussion about relationship to the pendulum laboratory. Is this a good model of that damping?

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