1. Use Laplace transforms to solve the following differential
equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each
case.
i. 0 = ?̈(?) + 2?̇(?) + 4?(?)
ii. 0 = ?̈(?) + 3?̇(?) + 2?(?)
iii. 5 = ?̈(?) + 5?̇(?) + 6?(?)
3. For the three differential equations from problem one
determine the steady-state value of the system using:
a. lim?→0 ??(?),
b. lim ?→∞ ?(?) analytically,
c. lim ?→∞ ?(?)...