Find the response of a viscously damped system under the periodic force whose values are given in Problem 1.116. Assume that \(M_{t}\) denotes the value of the force in newtons at time \(t_{i}\) seconds. Use \(m=0.5 \mathrm{~kg}, k=8000 \mathrm{~N} / \mathrm{m}\), and \(\zeta=0.06\).

Data From Problem 1.116:-

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The torque (M) variation with time, of an internal combustion engine, is given in Table 1.3. Make a harmonic analysis of the torque. Find the amplitudes of the first three harmonics. TABLE 1.3 t(s) M, (N-m) t(s) M(N-m) t(s) M, (N-m) 0.00050 770 0.00450 1890 0.00850 1050 0.00100 810 0.00500 1750 0.00900 990 0.00150 850 0.00550 1630 0.00950 930 0.00200 910 0.00600 1510 0.01000 890 0.00250 1010 0.00650 1390 0.01050 850 0.00300 1170 0.00700 1290 0.01100 810 0.00350 1370 0.00750 1190 0.01150 770 0.00400 1610 0.00800 1110 0.01200 750