[40 Marks] Qn1 For an under-damped system in a state of longitudinal vibrations, the displacement equation is given by x = Ce Cos(@t-0) Where C and 0 are constants dependent of the initial conditions. (a) Given that at time't' = 0, x = 0, and the velocity is Vo, determine C and 0, and hence the complete displacement equation. [22 Marks] (b) For a mass of 12kg, a spring having a stiffness of 15 kN/m and a dashpot with a damping resistance of 550 Ns/m, determine the corresponding displacement equation. [10 Marks] (c) By considering the periodic time, determine the displacement after one cycle of oscillations and hence the logarithmic decrement of the system. [8 Marks] [40 Marks]