Let > 0, T > 0 and A be constants, and consider the mass-spring system for y(t) subject

to a delta function forcing, modeled by

y + (^2)y = A(t T)

for t>=0 withy(0)=1 andy(0) = -1

i) Calculate the solution using the Laplace transform.

ii) Set=1 and show that one can chooseAandT so thaty(t)= 0 for allt>T.