Based on the spring-mass system in Figure,
i. Derive the equation of motion, using Newton’s second law of motion.
ii. Derive the stiffness matrices of the spring-mass system assuming that all thecontacting surface are frictionless.
iii. Find the natural frequencies of the system, if k1 = k2 = k3 = k4 = k andm1 = m2 = m3 = m
iv. Using the Dunkerley method, determine the first natural frequency for the systemin Figure 1, if k1 = k2 = k3 = k4 = k and m1 = m2 = m3 = m.
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