Question

A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system equation found in part (a) to compute the frequency response Xss (t) if the input force is Sa(t) = 7 sin(76) N. Note that to do this, you have to find the transfer function and sinusoidal transfer function for the system. c) Determine the input frequency w that results in the largest steady-state amplitude of the mass displacement You are required to show all the steps involved in finding your final answer, even the smallest details. Make sure in your final answer, all numerical values are substituted and equations are simplified to the simples form.

Answer 1

Giveni SDOF dampead flouced letration. Analgin bix mit memelihat bia 4.4 eft): a sinet) ^ 1^ kx M-03 10=R R$ Wh2= o.s mm Ft). (FBD2 @ COURO wing Newton 2 law, mi + Rx +(61+62) 8 = f(t) 0.3x + lov + 4.9% = 7 sen ett). O PF XO) fo) Taking lapsou all o 6.38+10 +4.49) X(A) = f(e) = IF 2 F) (0-35+10+4.959 Soluing and @ in line domain, Xos(t) = 0·029.1 cm (7-66:52°) B from input feequery in taxfest amplettide is 'w' equal to that results to not free wn = 5:77, wn nell Mej 10/0.3 W = 5.77 rad /s response is is at so naam steady stat amplitude W =wn sitt rolls

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