Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped
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In the previous video in the playlist we saw undamped harmonic motion such as in a spring that is moving horizontally on a frictionless surface just due to Hooke's law. In this video we upgrade and consider friction as well. We get a second order differential equation that is a constant coefficient homogeneous and we know how to solve these. However, qualitatively the type of solution you get depends on the constants. In the cast of underdamped, you get oscillations that decay exponentially. In the case of overdamped, that is too much friction, then it is just exponential decay with no oscillations possible. And then there is the very interesting third case of critically damped that gives a repeated root to the characteristic equation.
0:00 Deriving the ODE
1:58 Solving the ODE (three cases)
3:20 Underdamped Case
5:20 Graphing the Underdamped Case
7:33 Overdamped Case
8:50 Critically Damped
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