The following figure shows a machine of mass m mounted on a vibration isolator. The machine(starting at rest at t=0) is subjected to a sinusoidal excitation force p(t) = P sin wt. Solve forthe transfer function X(s)/P(s). Then state in words the process you would then follow todetermine the force transmissibility, TR.p(t) = P sin wimb₂

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Answered: The following figure shows a machine of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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1. Consider the simplified model we discussed in class about a car on a bumpy road. The car has a mass m supported by stiffness k and damping c. The road gives a displacement excitation R(t) to the car. The transfer function from R(t) to the car displacement y(t) is Hy(s) - Y(s) R(s) cs + k ms² + cs+k (1) (a) Determine the driving point impedance ZR(s), which is the ratio of the velocity R(t) to the force acting on the wheel from the road. (b) Engineer X is testing the car in the Vehicle Dynamics Lab of a start-up company GF.com. Because of insufficient cash flow, Engineer X only has the equipment to mea- sure ZR(s), and identify the zeros and poles of ZR(s). But eigineer X wants to find the poles of Hy(s). To do so, should Engineer X use the zeros or poles of ZR(s) instead? Explain why? m y(t) R(t) Figure 1: A simple model of a car on a bumpy road
4) Consider the system below. Write the equation of motion and calculate the response assuming that the system is initially at rest for the values k₁ 100[N/m], k2= 100[N/m], k3 = 200[N/m], 100[N/m], k5 = 50[N/m], k6: 50[N/m], and m = = [10kg]. Solve the equation of motion k4 = as a differential equation = F(t) = 80 cos (20t) K5 Κι www K3 ΚΑ m www K6 K2
3. Consider the vibrating system described below (t) 4 -2 -2 1 [ói]x+ [ $ ? ]x= 11 * 0 Compute the mass - normalized stiffness matrix, the eigenvalues, the normalized eigenvectors, the matrix P, and show that PTP I and PTKP is the diagonal matrix of eigenvalues A.
2) Consider the spring-mass-damper system hanging down from a ceiling. Initially, the system is at rest. Then, we gently place another mass (M) on top the original one (m). First, please obtain the equation of motion of the mass m in the system (before we placed the other object). Assign the displacement references yourself and obtain the equation accordingly. From the equation of motion, please obtain the transfer function, G(s), between an external force on the mass m , f(t), and the displacement of the mass m, x(t). Then, please obtain the motion of the object M, using the transfer function G(s). Don't forget that G(s) belongs to the system shown on the top! To solve this, represent the force applied by the added mass (M) as a function of time. How would you describe the act of adding a mass as an external force input? Then solve for x(t). c = 10 Ns/m k = 50 N/m m = 5 kg M M = 25 kg F(s) G(s) X(s)
PLS PROVIDE ME WITH THE COMPLETE SOLUTION
Look at the below system. Assume that the forcing function is a sine and cosine response (i.e., F = Focos(wt) and F = Fösin(wt)). If your system has the following variables: m= K= 15 kg 207 F₁ = 168 w = w₁/2 Xo = 1 m/s Vo = -1 m/s Plot both responses of the system.
:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k

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