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3.23 The system shown in Figure P3.23 is acted upon by the forcing function shown. The system parameters are m = 15 kg, k = 75 kN/m,fo = 750 N, and o 15.13 Hz. Tasks: For motion about equilibrium, determine the steady-state amplitude and phase: (a) Free vibration tests result in a log dec, 6, of Im 0.523 (b) c=0. (c) Using the damping from part (a), determine ft)-fo cos ot the range of excitation frequencies such that the amplitude is 20 mm or less FIGURE P3.23

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Q.A Solution - Kresurs K,+K2 (Spring in paralled) = 75+75 = 150 kN/m = 150x1o®N/m & force of ison f=W=15.13H3: ; Le = 206 =.9<by Golution: - c=0 S=C F0 2 mwa => A= Folkresult V[1-(49.133 * (25 4, = 750/150X109) Isi-195.0687 Tre loo HA=0.051 m Avy ...Solving above equation, w?= 7986.19952 .?W=89.365 rad/s = 14.22 Hz Ay ... The excitation frequency is up!4.22 Hazi

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