Question 1 A 2kg object is attached to a spring and will stretch the spring 612.5 mm by itself as shown in Figure Q1 below. Unstretched spring u(t): object displacement at

any time t mu" + ku = F(t) mg k= L u(0): intial displacement u' (0): initial velocity www System at rest Show that the IVP for this system is wwwwwwww Figure Q1: Spring mass system (Source: Google Image) Initial state Assume that there is no damping in the system and the force F(t) = 5 cos 4t is applied to the object and the system will experience resonance. The object is initially displaced 20 cm downward from its equilibrium position and given a velocity of 10 cm/sec upward. (a) 2u" + 32u = 5 cos 4t, u(0) = 0.2 and u' (0) = -0.1 u(0)=20cm (6 marks)/nMTH320 (b) (c) Hence find and sketch the object displacement at anytime t. Explain what will happen to the displacement as t → ∞o. Tutor-Marked Assignment (15 marks) (4 marks)