Solve the equations of motion using the Laplace transform approach:

(a) \(\ddot{x}+3 \dot{x}+2 x=u(t), x(0)=1, \dot{x}(0)=0\)

(b) \(2 \ddot{x}+5 \dot{x}+3 x=e^{-3 t}, x(0)=1, \dot{x}(0)=1\)

(c) \(\ddot{x}+2 \dot{x}+2 x=\cos t, x(0)=2, \dot{x}(0)=4\)

(d) \(\ddot{x}+2 \dot{x}+x=e^{-2 t}+\sin 2 t, x(0)=1, \dot{x}(0)=-1\)

(e) \(\ddot{x}-2 \dot{x}+3 x=t, x(0)=0, \dot{x}(0)=2\).