Answer Happy

Consider Fig 1 (a) and (b) showing an SDoF and MDoF systems. C1 C2 mi ki k2 Figure 1(a). SDoF system C2 C4 C1 k2 m2 mi ki k4 w w will Figure 1(b). MDOF system.
d. Assume that the masses are m = 0.2 kg and m2 = 0.1 kg; the stiffness constants are ki = 1 kN/m, k2 = 2 kN/m, and kz = 0.5 kN/m; and the = damping constants c1 = C2 = cz = 0.05 kN. s/m. Calculate the eigenvalues and eigenvectors of the MDPF system in Fig 1(b). [10] e. Given that a sinusoidal force f(t) = Fı sin(7īt) is applied on mass mi, calculate the time responses of the SDoF system and the MDF systems at time t = 2 s. Assume that the initial displacements and velocities are X10 = 5 mm and V10 = 0 mm/s for mass mj; and X20 = 1 mm and V20 = 0 mm/s for mass m2. [15] f. Calculate the FRF value at a frequency of w = 22 rad/s. [5] g. Why are accelerometers preferred in vibration measurements compared to displacement and velocity sensors? [2] h. Why is vibration measurement important? Concisely discuss this with respect to any two important applications in vibration measurements. [8]