Chapter 16, Problem 56RE

a)

To determine

To calculate: The solution of the differential equation, $\frac{8}{32}y\text{'}\text{'}\left(t\right)+by\text{'}\left(t\right)+ky\left(t\right)=\frac{8}{32}F\left(t\right)$. Also graph the solution for each of the assigned quantities for b, k, F(t) using graphing utility.

$b=0,k=1,F\left(t\right)=24\sin \pi t$

$b=0,k=2,F\left(t\right)=24\sin \left(2\sqrt{2}t\right)$

$b=0.1,k=2,F\left(t\right)=0$

$b=1,k=2,F\left(t\right)=0$

b)

To determine

The effect of increasing resistance to the motion b.

c)

To determine

How the motion of the object changes when a stiffer spring (greater value of k) is used.