Question - Consider the spring-mass system whose motion is governed by the initial value problem (IVP):
y'' + 4y' + 13y = cos(t), y(0) = 0, y'(0) = 1, where y is the displacement from equilibrium in feet and t is the time in seconds.
(a) Use the method of undetermined coefficients to find the particular solution. Write your answer in the form yp(t) = Rcos(t-δ). Show the solution steps.
(b) Verify your answer in (a) by using the formula for yp, and δ on the Formula Sheet (or in the text). Give exact values as well as decimal approximates, round to two decimal places.
(c) Solve the IVP.