QUESTION 3 : Given g(t) = { 0st...

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QUESTION 3 : Given g(t) = { 0st<T, t2T. sin t, Express g(t) as a combination of unit step function and show that the Laplace transform of g(t) is given by i. L{g(t)} s2. ii. Determine |s(s2 + 1). ii. Determine e L-1 T? + 1)2 iv. Hence, using L{g(t)} in (i), solve the following initial value problem y" +y = g(t). y(0) = 0, /(0) = 0. %3D QUESTION 3 : Given g(t) = { 0st<T, t2T. sin t, Express g(t) as a combination of unit step function and show that the Laplace transform of g(t) is given by i. L{g(t)} s2. ii. Determine |s(s2 + 1). ii. Determine e L-1 T? + 1)2 iv. Hence, using L{g(t)} in (i), solve the following initial value problem y" +y = g(t). y(0) = 0, /(0) = 0. %3D