Solution for Forced Vibration of a Damped SDOF System

In this example, we are looking into a damped SDOF system subjected to forced vibration while having initial displacement and velocity. 

The solution for the dynamic responses of the system starts with the selection of suitable solution for transient response based on the damping ratio of the system. The frequencies of the system are then calculated to apply the solution.

Then, the external force characteristics are used to aid in the determination of steady state response. By adding up both transient and steady state responses, we obtain total response of the system.

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

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

System overview

Solution for transient response

Solution for steady state response

Graph of displacement responses against time