A mass spring system with two masses and three springs is described by the linked first order ODEs in Equations (2.1) and (2.2), x; and x2 represent the displacement from equilibrium of each respective mass, and t represents time. dx - M +(K + K)x Kx = 0 dt M +(K + K3)x - Kx = 0 dx dt Equation (2.1) M: has a mass of 1 kg, M a mass of 2 kg, K: a spring constant of 1 kg s, K a spring constant of 2 kg s and K3 a spring constant of 2 kg s. (a) Equation (2.2) Substitute the given values into the coupled ODEs in Equations (2.1) and (2.2). (4 Marks) (b) Take the Laplace transform of Equation (2.1), given x:= -1, x2 = 2, and dx=dx2=0 at t = 0. (6 Marks) dt dt (c) Take the Laplace transform of Equation (2.2), given x; = -1, X2 = 2, and dx=dx=0 at t = 0. (6 Marks) dt dt X (s) = (d) Taking your answers for part b) and part c), show that solving for X gives the equation shown in equation (2.3). (6 Marks) 2s + 5s (s + 4)(s + 1) Equation (2.3) (e) Resolve equation (2.3) into partial fractions. (6 Marks)