QUESTION 5 (a) Define the term Magnification Factor (MF) and explain why it is important to...

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QUESTION 5 (a) Define the term Magnification Factor (MF) and explain why it is important to determine the Magnification Factor (MF) of a system. [CO1/PO1/C2] (5 marks) (b) Figure Q5(a) shows a system of three masses m, m and m3, which is attached to a tightly extendable string with consistent tension T, fixed at both ends with m =m3 = m and m = 2m. The length of each string is such that 1 = l = l3 = l. Assuming the tension does not vary with transverse motion, (i) determine the stiffness influence matrix of this system, and, (ii) estimate the natural frequency of this system. [CO2/PO3/C4] (10 marks) 12 Lumin 13 14 mi m2 m3 Figure Q5(a) r (c) A simple undamped spring-mass system as shown in Figure Q5 (b) is set into motion from rest by giving an initial displacement. Obtain the equation of motion of the system by using x as the generalized coordinate. and find its natural frequency. Given disk of radius, r = 0.1 m, mass, m = 1 kg and spring stiffness, k = 1000 N/m. [CO3/PO3/C6] (5 marks) (Roll without slip) Figure Q5 (b) X1 X2 X3 X k 1 QUESTION 5 (a) Define the term Magnification Factor (MF) and explain why it is important to determine the Magnification Factor (MF) of a system. [CO1/PO1/C2] (5 marks) (b) Figure Q5(a) shows a system of three masses m, m and m3, which is attached to a tightly extendable string with consistent tension T, fixed at both ends with m =m3 = m and m = 2m. The length of each string is such that 1 = l = l3 = l. Assuming the tension does not vary with transverse motion, (i) determine the stiffness influence matrix of this system, and, (ii) estimate the natural frequency of this system. [CO2/PO3/C4] (10 marks) 12 Lumin 13 14 mi m2 m3 Figure Q5(a) r (c) A simple undamped spring-mass system as shown in Figure Q5 (b) is set into motion from rest by giving an initial displacement. Obtain the equation of motion of the system by using x as the generalized coordinate. and find its natural frequency. Given disk of radius, r = 0.1 m, mass, m = 1 kg and spring stiffness, k = 1000 N/m. [CO3/PO3/C6] (5 marks) (Roll without slip) Figure Q5 (b) X1 X2 X3 X k 1

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