Three particles, B, C and D, of masses m, ½m and m, respectively, are connected to three springs as shown in the following figure. A 2k, lo 3k, lo m k, lo m M -000000000 000000000 B D The left-hand spring is connected to a fixed point A, and the particles are constrained to move in a straight line on a smooth horizontal surface. Each spring has natural length lo. Spring AB has stiffness 2k, spring BC has stiffness 3k, and spring CD has stiffness k. The particles are displaced from their equilibrium positions and released. The displacements of the particles B, C and D from their equilibrium positions are x1, x2 and x3, respectively, and time t is measured from the instant when the particles are released. (a) Draw a force diagram showing all the forces acting on each particle. (b) Copy and complete the following table to give the change in spring force from equilibrium for each spring acting on each particle. The notation is the same as that used in the unit. Spring Particle Extension Stiffness S ΔΗ AB B BC B BC C CD C CD D (c) Hence derive the equation of motion for each particle, and show that in matrix form, these equations may be expressed as k -5 3 0 (1)-(+)) (@) #2 3 = m 6-8 0 2