taking L.T.,,,,,,,,,,,,Y(s)[s^2+4s+14]=L(T(t))...........for periodic functions the trans form is given as ........inte(0 to T)(T(t))exp(-st)*dt/[1-exp(-sT)].........solving we get the the integral as [(1+exp(-s)-2*exp(-s/2)/s^2.+ (exp(-s)-exp(-s/2))/s]...........putting it in the equation we get [(1+exp(-s)-2*exp(-s/2)/s^2.+ (exp(-s)-exp(-s/2))/s]/([s^2+4s+14]) Solution taking L.T.,,,,,,,,,,,,Y(s)[s^2+4s+14]=L(T(t))...........for periodic functions the trans form is given as ........inte(0 to T)(T(t))exp(-st)*dt/[1-exp(-sT)].........solving we get the the integral as [(1+exp(-s)-2*exp(-s/2)/s^2.+ (exp(-s)-exp(-s/2))/s]...........putting it in the equation we get [(1+exp(-s)-2*exp(-s/2)/s^2.+ (exp(-s)-exp(-s/2))/s]/([s^2+4s+14]).