Chapter 5.3, Problem 26E

(a)

To determine

To graph: The function $g\left(\gamma \right)=F/\sqrt{\left({\omega }^2-{\gamma }^2\right)+4{\lambda }^2{\gamma }^2}$ for $k=4,m=1,F=2$, and the damping coefficient $c=2,1,0.75,0.50\text{ and }0.25$.

(b)

To determine

To graph: The function $g\left(\gamma \right)=F/\left({\omega }^2-{\gamma }^2\right)+4{\lambda }^2{\gamma }^2$ for $k=49,m=10,F=20$, and the damping coefficient $c=2\lambda =2,1,0.75,0.50,\text{and}0.25$ and find the maximum magnitude of $g\left(\gamma \right)$ when $c\to 0$ and explain how the resonance frequency relates to the natural frequency when $c\to 0$.