2000 ki mi T ()'x 2000 m2 T X26) 00000 Figure Q2 Q2 A mass-spring system is shown in Figure Q2 with mi = 10 kg, m2 = 2

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2000 Ki Mi T X 2000 M2 T X26 00000 Figure Q2 Q2 A Mass Spring System Is Shown In Figure Q2 With Mi 10 Kg M2 2 1 (10.09 KiB) Viewed 17 times

Note that :
P - 2
Q- 9
R - 6

2000 Ki Mi T X 2000 M2 T X26 00000 Figure Q2 Q2 A Mass Spring System Is Shown In Figure Q2 With Mi 10 Kg M2 2 2 (30.04 KiB) Viewed 17 times

2000 ki mi T ()'x 2000 m2 T X26) 00000 Figure Q2

Q2 A mass-spring system is shown in Figure Q2 with mi = 10 kg, m2 = 20 kg, kı = (10+P) N/m, k2 = (10+Q) N/m and k3 = (20+R) N/m. (a) If the system is made to vibrate freely in vertical direction, draw a free body diagram for the system (4 marks) (b) Proof that the equation of motion for the system as: [m, O Sky + kg) -ky Vxl 0 m2JX2 -k (ką +k;)] X2 (6 marks) (c) Determine the natural frequencies of the system. (7 marks) (d) Evaluate and illustrate the mode shapes of the system. (8 marks)