From a situation where a damped SDOF system is subjected to free vibration, we can derive the definition for critical damping and the angular frequency of that damped system. Based on the value of damping ratio, three possible cases may occur: critical damping, overdamping and underdamping. For both critical damping and overdamping cases, the movement of system will be stopped immediately.
Click here to download our excel worksheet we use to plot the graph of displacement response against time.
The following shows the theory for free vibration of a damped SDOF system. Watch the video above for full details.
Equilibrium equation for damped SDOF system subjected to free vibration
Derivation 1
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Derivation 13
Graph of displacement against time
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