Vibrations FreeForced UndampedDampedUndampedDamped

Transient Vibrations of Single Degree of Freedom Systems Single Degree of Freedom System with an applied force f(t): where f(t) can be of any form.

Equation of Motion: Solution:

Solution for a General Force F(t):

Example:

Excitations Changing at Discrete Times: A step force f(t) starting at t = 0:

A step force f(t) starting at t = t 0 : In general, we have the convolution integral:

Some Excitations Given in Figure 4.5:

Response of an Undamped Single-Degree-of-Freedom System:

Transient Motion due to Base Excitation: x: Displacement of system y: Displacement of base Equation of Motion : Defining z = x  y, we get Or,

Solution with Convolution Integral :