Solution for Free Vibration of Damped SDOF System

This is an example showing the solution for a damped SDOF system subjected to free vibration. In this example, we demonstrate the way to calculate the damping coefficient of the system. Then, by calculating the natural frequency and angular frequency of the damped system, we can determine the expressions for the dynamic responses of the system. From these expressions, we get to plot the graph of dynamic responses against time.

Click here to download our excel worksheet for free vibration of a damped SDOF system.

The following shows the solution for free vibration of a damped SDOF system. Watch the video above for full details. 

Undamped SDOF system overview

Derivation of solution for dynamic responses for underdamped SDOF system

Solution for damping coefficient

Solution for natural frequency and angular frequency of the damped system

Expressions for dynamic responses

Displacement-time graph

Velocity-time graph

Acceleration-time graph

Dynamic responses after 5 seconds