Skill-Assessment Exercise 2.8PROBLEM: Find the transfer function, G(s) = X2(s)/F(s), for the translationalmechanical system shown in Figure 2.21.▬▬▬fv₁² = 1 N-s/mf(t)fv,= 1 N-s/mx1 (t)M₁ = 1 kgK= 1 N/moooofv₂ = 1 N-s/mx2 (1)M₂ = 1 kg= 1 N-s/mfv₂=FIGURE 2.21 Translationalmechanical system for Skill-Assessment Exercise 2.8

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Answered: PROBLEM: Find the transfer function,…

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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6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
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)
1. Find the transfer function, c(s) - X;(s)/F(s), for each of the system shown In the figure below. a. K-5 Nim Ad, = 5 kg -3Nslm K=4 Nim M=4 ky M =5 kgAn K=4 N/m Siy - 2 N-sm Frictionless Sy =4N-s/m K-5 N/m e = 4N-s/m M4 kg 00O -M2 = 4 kg foy=4 N-s/m Sv4 N-s/m
9. Derive the transfer function X₂ (s)/F(s) for the mechanical system shown in Figure 2. Assume the following values: M₁ = 3 kg, M₂ = 2 kg, K₁ = 5 N/m, K₁= 3 N/m, D₁ = 1 N.s/m, K₁ oooo OH M₁ oooo K₂ Figure 2 M₂ 1(1)
4. Obtain the transfer function for the following mechanical rotational system TM O (s) T= Ty(s) T3 BL Load
Find the transfer function G(s) =X2 (s) /F (s), for the translational mechanical system shown in Figure (b). x1(1) x2(t) 1 N/m f() I kg 1 N-s/m 1 kg Frictionless Figure. (b)
4. The mechaincal system is shown in the figure. Assume X₁> X2. a) Draw the free body diagram and write all of the elemental equations. b) Write the equation of motion c) Find the transfer function of the system. F(s) is the input, X₁(s) is the output. K₁ K₂ m f(t) X₂ X1
X2(s) 8 Find the Transfer Function G(s) = for the trans- lational mechanical system shown in the Figure. (Hint: place a zero mass at r2(t)). ell 10 kg 2 N/m 5 N-s/m 2 N-s/m 9 For the system in the Figure below, find the Transfer Function G(s) = X1(s) F(s) K= 4 N/m K2= 5 N/m 3 N-s/m M =I kg rz=3 N-s/m M2 = 2 kg fr 2 N-s/m
Problem Consider the following mechanical system consisting of a massless rod of length L connected to a ball of mass m. The system has a rotational damper b, a spring constant k, and is subject to gravitational acceleration g. The input into the system is a torque u(t). 4 torque input u(t) 10 L Lamb.. 'm k Derive and fully simplify the transfer function: gravity (s) U (s) G(s) Make sure to expand/cancel terms such that the numerator and denominator are each a polyno- mial in terms of s (with coefficients in terms of the constants of the problem: k, m, b, L as needed). Use small angle approximations.
Find the transfer function, X2(s)/F(s) For the system show in the figure.
Obtain the transfer function X(s)/X(s) of the mechanical system shown in Figure 3-23(a). Also obtain the transfer function E(s)/E(s) of the electrical system shown in Figure 3-23(b). Show that these transfer functions of the two systems are of identical form and thus they are analogous systems R: R (a) (b) ww- ww-
A liquid storage system is shown below. The normal oper-ating conditions are q1=10 ft3∕min,q2=5ft3∕min,h=4ft.The tank is 6 ft in diameter, and the density of each stream is 60 lb/ft3. Suppose that a pulse change in q1 occurs as shown inFig.(a)What is the transfer function relating H′ to Q′1?(b)Derive an expression for h(t) for this input change.(c)What is the new steady-state value of liquid level h?(d)Repeat (b) and (c) for a change in q1 from 10 to 20 (at t=0) to 15 ft3/min at t=12

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