System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 4.70P
Figure P4.70 shows a quarter-car model that includes the mass of the seats (including passengers). The constants
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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
Vibration Engineering. Please help to answer this problem. Show complete solution. Thanks will upvote after
You are requested to design an automotive suspension or
shock absorber system. In order to simplify the problem to one
dimensional multiple mass-spring-damper system, a quarter vehicle
model is used. The system parameters and free-body diagram of such
system is shown below.
M₁: Automobile body mass
M₂: Wheel and suspension mass
K₁: Spring constant of suspension system
K2: Spring constant of wheel and tire
B: Damping constant of shock absorber
(a) Obtain the transfer function of
X₁ (s)
F(s)
T₁(s) =
= 2500 kg
= 320 kg
and T₂(s) =
= 80,000 N/m
= 500,000 N/m
= 350 N-s/m
Automobile-
Suspension
system
Wheel-
M₁
M₂
X₁ (s) - X₂ (S)
F(s)
in terms of the parameters of mass, damper and elastance (M, B and K).
(b) Express the T₁ (s) and T₂ (s) with numerical values.
c) Plot the x₁ (t) and x₁ (t) = x₂(t) outputs of this passive suspension system for the input torque
f(t) = 2,000 N.
fit) K₂
x₂(t)
-Tire
Chapter 4 Solutions
System Dynamics
Ch. 4 - Prob. 4.1PCh. 4 - In the spring arrangement shown in Figure P4.2....Ch. 4 - In the arrangement shown in Figure P4.3, a cable...Ch. 4 - In the spring arrangement shown in Figure P4.4,...Ch. 4 - For the system shown in Figure P4.5, assume that...Ch. 4 - The two stepped solid cylinders in Figure P4.6...Ch. 4 - A table with four identical legs supports a...Ch. 4 - The beam shown in Figure P4.8 has been stiffened...Ch. 4 - Determine the equivalent spring constant of the...Ch. 4 - Compute the equivalent torsional spring constant...
Ch. 4 - Plot the spring force felt by the mass shown in...Ch. 4 - Calculate the expression for the natural frequency...Ch. 4 - Prob. 4.13PCh. 4 - Obtain the expression for the natural frequency of...Ch. 4 - 4.15 A connecting rod having a mass of 3.6 kg is...Ch. 4 - Calculate the expression for the natural frequency...Ch. 4 - For each of the systems shown in Figure P4.17, the...Ch. 4 - The mass m in Figure P4.18 is attached to a rigid...Ch. 4 - In the pulley system shown in Figure P4.19, the...Ch. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - In Figure P4.23, assume that the cylinder rolls...Ch. 4 - In Figure P4.24 when x1=x2=0 the springs are at...Ch. 4 - 4.25 In Figure P4.25 model the three shafts as...Ch. 4 - In Figure P4.26 when 1=2=0 the spring is at its...Ch. 4 - Prob. 4.27PCh. 4 - For the system shown in Figure P4.28, suppose that...Ch. 4 - For the system shown in Figure P4.29, suppose that...Ch. 4 - Prob. 4.30PCh. 4 - For Figure P4.31, the equilibrium position...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - 4.34 For Figure P4.34, assume that the cylinder...Ch. 4 - Use the Rayleigh method to obtain an expression...Ch. 4 - Prob. 4.36PCh. 4 - 4.37 Determine the natural frequency of the system...Ch. 4 - Determine the natural frequency of the system...Ch. 4 - Use Rayleigh's method to calculate the expression...Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - The vibration of a motor mounted on the end of a...Ch. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - A certain cantilever beam vibrates at a frequency...Ch. 4 - Prob. 4.47PCh. 4 - 4.48 The static deflection of a cantilever beam is...Ch. 4 - Figure P4.49 shows a winch supported by a...Ch. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - 4.53 In Figure P4.53 a motor supplies a torque T...Ch. 4 - Derive the equation of motion for the lever system...Ch. 4 - Prob. 4.55PCh. 4 - Figure P4.56a shows a Houdaille damper, which is a...Ch. 4 - 4.57 Refer to Figure P4.57. Determine the...Ch. 4 - For the system shown in Figure P4.58, obtain the...Ch. 4 - Find the transfer function ZsXs for the system...Ch. 4 - Prob. 4.60PCh. 4 - Find the transfer function YsXs for the system...Ch. 4 - Prob. 4.62PCh. 4 - 4.63 In the system shown in Figure P4.63, the...Ch. 4 - Prob. 4.64PCh. 4 - Figure P4.65 shows a rack-and-pinion gear in which...Ch. 4 - Figure P4.66 shows a drive train with a spur-gear...Ch. 4 - Prob. 4.67PCh. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Figure P4.70 shows a quarter-car model that...Ch. 4 - Prob. 4.71PCh. 4 - 4.72 Derive the equation of motion for the system...Ch. 4 - A boxcar moving at 1.3 m/s hits the shock absorber...Ch. 4 - For the systems shown in Figure P4.74, assume that...Ch. 4 - Refer to Figure P4.75a, which shows a ship’s...Ch. 4 - In this problem, we make all the same assumptions...Ch. 4 - Refer to Figure P4.79a, which shows a water tank...Ch. 4 - The “sky crane” shown on the text cover was a...Ch. 4 - Prob. 4.81PCh. 4 - Prob. 4.82PCh. 4 - Suppose a mass in moving with a speed 1 becomes...Ch. 4 - Consider the system shown in Figure 4.6.3. Suppose...Ch. 4 - Prob. 4.86PCh. 4 - Figure P4.87 shows a mass m with an attached...Ch. 4 - Figure P4.88 represents a drop forging process....Ch. 4 - Refer to Figure P4.89. A mass m drops from a...Ch. 4 - Prob. 4.90PCh. 4 - (a) Obtain the equations of motion of the system...Ch. 4 - Refer to part (a) of Problem 4.90. Use MATLAB to...Ch. 4 - Refer to Problem 4.91. Use MATLAB to obtain the...Ch. 4 - 4.94 (a) Obtain the equations of motion of the...Ch. 4 -
4.95 (a) Obtain the equations of motion of the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface in computer hard disk drives. The head has mass m and is supported by a suspension with stiffness k₁. Moreover, the moving disk surface will generate an air bearing lifting the head slightly above the disk surface (e.g., in the order of 20 nm). The air bearing is simplied as a linear spring with stiffness k2 and damping coefficient c. Let x(t) be the roughness of the disk surface and serve as the input excitation to the head/suspension system. Moreover, y(t) is the relative displacement of the head to the disk. In real hard disk drive applications, we want to keep y(t) almost constant, so that the head can follow the disk surface to perform read/write operations. (a) Show that the equation of motion is mi+cy + (k1 + k2) y = −mä – k₁x (2) 1 (b) Derive the frequency response function. Plot the magnitude and phase of the frequency response function. In plotting the frequency response…arrow_forward2. Duffing's equation is a model for a dynamic system that includes a damping term and a nonlinear stiffness term. It most notably describes dynamics of electrical systems, but it has a simple analog as a nonlinear vibrations problem. Derive the non-homogeneous Duffings equation below using Hamilton's Principle. Start from the definition of the kinetic energy of a unit mass, and the virtual work of the springs and damper. Note, the spring force terms are both derivable from an energy function. x+cx+kx+vx³ = F sin sin(at)arrow_forwardPlease solve the vibrations question 4.15 attached, Thank You!arrow_forward
- For each of the systems shown in Figure P4.52, the input is the force f andthe outputs are the displacements x1 and x2 of the masses. The equilibriumpositions with f = 0 correspond to x1 = x2 = 0. Neglect any friction betweenthe masses and the surface. Derive the equations of motion of the systems.arrow_forwardConsider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. Pell (P2 R2 P1 Pa ¡P3 R1 P4 L2 Li Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form. b. If you were to consider the input to the system to be the difference between the pressure on 0(s) either side of the piston, write the transfer function for the displacement of the piston: AP(s) Xj = 0 c. Develop the state equations for this system if the state variables are:arrow_forwardROTATION SYSTEM -ENERGY METHOD Q1-A mass m is connected to a spring of stiffness k through a string wrapping around a rigid- pulley of radius R and mass moment of inertia I. Derive the equation of motion for the system fig (1) by energy method , find Tn , time response of the system.arrow_forward
- Whats the first equation (circled) and how did we get it ?arrow_forward(a) A body of mass m, controlled by an elastic system, is given a displacement x. Derive an expression for the periodic frequency, n, of linear motion of the elastic system 1 n = Hz 1 Hz where ő is the static deflection in metres under the load, mg. (b) Figure TQ3.3 shows a suspended pendulum from a fixed pivot at O. The pendulum consists of a bar B, of mass 1kg, and block C of mass 6kg. The centre of gravity G1 and G2 of B and C are at distance 150mm and 375mm from 0. The radius of gyration of B and C, each about its own centre of gravity, are respectively 100mm and 25mm. A light spring is attached to the pendulum at point P, 200mm from 0, and is anchored at a fixed point, Q. When the Pendulum is in equilibrium, the line OG,PG2 is at 45° from the vertical and the angle OPQ is 90°. The spring has a stiffness of 700N/m. Calculate the natural frequency of the pendulum for small oscillations about the equilibrium position. 45° 0-150 0-20 Ig N G2 f0-3750 Y6g N Figure TQ3.3arrow_forwardThe nat. period of an undamped system is 3 s, but with a damping force that is proportional to the velcoity, the period becomes 5 s. Find the differential equation of motion of the system and its solution.arrow_forward
- A mechanical dynamic system is having two degrees of freedom as shown in figure 2. The given parameters are mass is 3 Kg, damping factors b;= 5 N-s/m, b2= 2 N-s/m and b3= 1 N- s/m, the spring constants k1= 3 N/m, k2= 6 N/m and k3= 2 N/m. Base on this diagram, determine the following. i. Draw and label complete Free Body Diagram of the network. ii. The differential equations representing the system. X2(s) F(s) iii. The transfer function iv. What is the effect connecting springs and damper in this configuratior. f(t) m2 b, b, b, Figure 2arrow_forwardIn the system in the figure, the static equilibrium position of the thin, slender homogeneous rod of mass m and length L is horizontal.During the movement of the system, the bar is separated from the horizontal by small angles. (A makes oscillating motion with small angles relative to the simple support point)a) Find the equation of motion of the system in terms of the given parameters.b) Since M=4 kg, m=1 kg, L=1 m, k=600 N/m, c=200 Ns/m, F=300 N, w=4 rad/s, is there resonance in the system? If there is resonance, what would you recommend to get rid of resonance?arrow_forwardPlease help me on this question. Thank u!arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Undamped Free Vibration of SDOF (1/2) - Structural Dynamics; Author: structurefree;https://www.youtube.com/watch?v=BkgzEdDlU78;License: Standard Youtube License