I’m studying and need help with a Mathematics question to help me learn.

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:y’(t)=1 –sin(t) with y(0) = 0.