Question 1 A 2kg object is attached to a spring and will stretch the spring 612.5 mm by itself as shown in Figure Qi below. u(t): object displacement at any time t mu" + ku = F(t) Unstretched spring MTH320 (b) u(0): intial displacement (0): initial velocity (c) 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. SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUS) System at t Figure Q1: Spring mass system (Source: Google Image) Show that the IVP for this system is wwwwwwww 2u" +32u = 5 cos 4t, u(0) = 0.2 and u'(0) = -0.1 Hence find and sketch the object displacement at anytime t. Explain what will happen to the displacement as t → . (0)-20cm (6 marks) Tutor-Marked Assignment (15 marks) (4 marks)

Fig: 1