Question VIII (a) Compute the Laplace transform of the function fa(t) = (Ma - Wa+1 ) sin it when a 2 0 is even. Hint: Use the fact that sin(x + 2x) = sina and sin(x + 7) = - sinx. (b) Compute the Laplace transform of the function fa(t) = (Wa - Wa+1 ) sinat when a 2 0 is odd. (c) Hence compute the Laplace transform of the function f(t) = | sin at). Hint: Use the fact that 1 + 2e- + 2e-2 + 2e-3 + ... = (1+ e-$)/(1 - e-s)