Fig. 1.1.8: Time response showing under-damped, over-damped and critically damped system. Here,

Fig 1.1.8 shows the time response of a system with Mass m =1, stiffness K=1000w/m for 3 different values of damping representing underdamped, critically damped and overdamped system.

Forced vibration response

For an under damped system the solution of the above equation is given below.

.......................(1.1.19)

Exercise Problem

1. Using principle of superposition check whether the following systems are linear or nonlinear.

(a)

(b)

(c)

(d)

(e)

2. Write a Matlab code to plot the response of a spring-mass-damper system subjected a harmonic force . Take