Questions:
1. Using the Laplace Transform, obtain the solution of the following differential equations:
i) y¨ + 4y = 4t, given that y(0) and y·(0) = 5
ii) y¨ + y = e-t, given that y(0) = 1, and y·(0) = 0
iii) y¨ + 4y = 3 cos 2t, given that y(0) = 1, and y·(0) = 0
iv) y¨ + y· + y = 0, given that y(0) = 1, and y·(0) = 0
2. Given a spring mass damper system as follows
y''(t) + 5y'(t) + 6y(t) = u(t)
Find its corresponding transfer function G(s) of this system.
3. Find the solution of
y¨ + 2y· - y = f(t), given y(0) = A, y·(0) = B
for the arbitrary constants A and B; and function f(t).