Solve the following differential equations using Laplace Transforms. Perform partial fractions using the residual method shown in class. 1.
x^(?) x=sin(t)
x(0)=0
x^(¨) 3x^(?) 2x=0
x(0)=0
x^(?)(0)=1
x^(¨) 2x^(?) x=0
x(0)=1
x^(?)(0)=1
x^(¨) \omega _(n)^(2)x=0
x(0)=x_(0)
x^(?)(0)=v_(0)