Question

Consider the initial value problem $my''+cy'+ky=F(t)$, $y(0)=0$, $y'(0)=0$, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force $F(t)$, where the unit of force is the Newton (N). Assume that $m=2$ kilograms, $c=8$ kilograms per second, $k=80$ Newtons per meter, and $F(t)= 40 \sin(6t)$ Newtons. 1. Solve the initial value problem. $y(t)=?$ 2. Determine the long term behavior of the system. Is $\lim_{t \to \infty} y(t)=0$? If it is, enter zero. If not, enter a function that approximates $y(t)$ for very large positive values of $t$. For very large positive values of $t$, $y(t)$ is approximately..?

          Consider the initial value problem $my''+cy'+ky=F(t)$, $y(0)=0$, $y'(0)=0$, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force $F(t)$, where the unit of force is the Newton (N). Assume that $m=2$ kilograms, $c=8$ kilograms per second, $k=80$ Newtons per meter, and $F(t)= 40 \sin(6t)$ Newtons.

1. Solve the initial value problem. $y(t)=?$

2. Determine the long term behavior of the system. Is $\lim_{t \to \infty} y(t)=0$? If it is, enter zero. If not, enter a function that approximates $y(t)$ for very large positive values of $t$. For very large positive values of $t$, $y(t)$ is approximately..?

Added by Timothy P.

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