# differential equations homework on webassign 9

I need someone to solve this for me please?

*Rewritey(t) = -1/2 sin(3t) + 2cos(3t) to Simple Harmonic Formy(t) = A sin()**A 16-pound weight is attached to a 5-ft-long spring. At the equilibrium the spring measures 8.2ft. If the weight is pushed up and released from rest at a point 2ft above the equilibrium position, find the motion x(t) if the surrounding medium offers a dumping resistance numerically equal to the velocity and the system is being driven by an external force f(t) = sin(t).*

*(Keep the exact value of amplitude A as the fraction with the square root.)*

*Answer: y(t) = _____________________________________________________________*

*1. Find the inverse of Laplace transform for f(t):*

* L ^{– 1 }*

**{**

*}=*^{ }*f(t ) = _______________________________________________________,**Then, f (1) = _________________________, f(3) = ___________________________________. *

*2.Solve for y(t) from the integral equation:yâ€™(t)=1 â€“sin(t) with y(0) = 0.*

*Answer:y(t) =__________________________________________________________________*

* *

*Solve for y(t):yâ€ + 16y=f(t)=***{***with y(0) = 0 and yâ€™(0) = 0.*