Question

3). Use the Laplace transform to solve for y(t) for t20. y(0 +) = 5, dt dt dt Initially relaxed dtdt

Answer 1

"d ^2 y/dt ^2 + 3 dy/dt + 2y = 0 y(d) = 5 dy(at)/dt = 0 y(0) Take laplace perform we get s ^2 y(s) - sy(0) - y^prime (0) + 3[sys - y(0)] + 2y (s) = 0 double rightarrow s ^2y(s) - 5s + 3 sy(s) - 3 times 5 + 24 (s) = 0 double rightarrow y(s) [s ^2 + 3s + 2] = 5s + 15 double rightarrow y(s) = 5s + 15/(s + 2) (s + 1) = A/s + 2 + 6/s + 1 {By using partial fraction} A = 5s + 15/s + 1