System Dynamics3rd EditionIII William J. Palm Publisher: MCGISBN: 9780073398068
System Dynamics
Solutions for System Dynamics
Problem 4.2P:
In the spring arrangement shown in Figure P4.2. the displacement x is caused by the applied force f....Problem 4.3P:
In the arrangement shown in Figure P4.3, a cable is attached to the end of a cantilever beam. We...Problem 4.4P:
In the spring arrangement shown in Figure P4.4, the displacement x is caused by the applied force f....Problem 4.5P:
For the system shown in Figure P4.5, assume that the resulting motion is small enough to be only...Problem 4.6P:
The two stepped solid cylinders in Figure P4.6 consist of the same material and have an axial force...Problem 4.7P:
A table with four identical legs supports a vertical force. The solid cylindrical legs are made of...Problem 4.8P:
The beam shown in Figure P4.8 has been stiffened by the addition of a spring support. The steel beam...Problem 4.9P:
Determine the equivalent spring constant of the arrangement shown in Figure P4.9. All the springs...Problem 4.10P:
Compute the equivalent torsional spring constant of the stepped shaft arrangement shown in Figure...Problem 4.11P:
Plot the spring force felt by the mass shown in Figure P4.11 as a function of the displacement x....Problem 4.12P:
Calculate the expression for the natural frequency of the system shown in Figure P4.12. Disregard...Problem 4.14P:
Obtain the expression for the natural frequency of the system shown in Figure P4.14. Discount the...Problem 4.15P:
4.15 A connecting rod having a mass of 3.6 kg is shown in Figure P4.15. It oscillates with a...Problem 4.16P:
Calculate the expression for the natural frequency of the system shown in Figure P4.16.Problem 4.17P:
For each of the systems shown in Figure P4.17, the input is the force f and the outputs are the...Problem 4.18P:
The mass m in Figure P4.18 is attached to a rigid lever having negligible mass and negligible...Problem 4.19P:
In the pulley system shown in Figure P4.19, the input is the applied force f, and the output is the...Problem 4.23P:
In Figure P4.23, assume that the cylinder rolls without slipping. The spring is at its free length...Problem 4.24P:
In Figure P4.24 when x1=x2=0 the springs are at their free lengths. Derive the equations of motion.Problem 4.25P:
4.25 In Figure P4.25 model the three shafts as massless torsional springs. When the springs are at...Problem 4.26P:
In Figure P4.26 when 1=2=0 the spring is at its free length. Derive the equations of motion,...Problem 4.28P:
For the system shown in Figure P4.28, suppose that k1=k , k2=k3=2k , and m1=m2=m . Obtain the...Problem 4.29P:
For the system shown in Figure P4.29, suppose that R2=2R1 , m1=m , and m2=2m . The two pulleys share...Problem 4.31P:
For Figure P4.31, the equilibrium position corresponds to x=0 . Neglect the masses of the pulleys...Problem 4.34P:
4.34 For Figure P4.34, assume that the cylinder rolls without slipping and use the Rayleigh method...Problem 4.35P:
Use the Rayleigh method to obtain an expression for the natural frequency of the system shown in...Problem 4.37P:
4.37 Determine the natural frequency of the system shown in Figure P4.37 using Rayleigh’s method....Problem 4.38P:
Determine the natural frequency of the system shown in Figure P4.38 using an energy method. The disk...Problem 4.39P:
Use Rayleigh's method to calculate the expression for the natural frequency of the system shown in...Problem 4.43P:
The vibration of a motor mounted on the end of a cantilever beam can be modeled as a mass-spring...Problem 4.46P:
A certain cantilever beam vibrates at a frequency of 5 Hz when a 30 Ib motor is placed on the beam....Problem 4.48P:
4.48 The static deflection of a cantilever beam is described by
where P is the load applied at...Problem 4.49P:
Figure P4.49 shows a winch supported by a cantilever beam at the stern of a ship. The mass of the...Problem 4.53P:
4.53 In Figure P4.53 a motor supplies a torque T to turn a drum of radius R and inertia I about its...Problem 4.54P:
Derive the equation of motion for the lever system shown in Figure P4.54, with the force f as the...Problem 4.56P:
Figure P4.56a shows a Houdaille damper, which is a device attached to an engine crankshaft to reduce...Problem 4.57P:
4.57 Refer to Figure P4.57. Determine the relations between , , and so that the damper shown in...Problem 4.58P:
For the system shown in Figure P4.58, obtain the equation of motion in terms of . The disk is a...Problem 4.63P:
4.63 In the system shown in Figure P4.63, the input is the force f and the output is the...Problem 4.65P:
Figure P4.65 shows a rack-and-pinion gear in which a damping force and a spring force act against...Problem 4.66P:
Figure P4.66 shows a drive train with a spur-gear pair. The first shaft turns N times faster than...Problem 4.70P:
Figure P4.70 shows a quarter-car model that includes the mass of the seats (including passengers)....Problem 4.72P:
4.72 Derive the equation of motion for the system shown in Figure P4.72. Assume small angles of...Problem 4.73P:
A boxcar moving at 1.3 m/s hits the shock absorber al the end of the track (Figure P4.73). The...Problem 4.74P:
For the systems shown in Figure P4.74, assume that the resulting motion is small enough to be only...Problem 4.75P:
Refer to Figure P4.75a, which shows a ship’s propeller, drive train, engine, and flywheel. The...Problem 4.76P:
In this problem, we make all the same assumptions as in Problem 4.75, but we do not discount the...Problem 4.79P:
Refer to Figure P4.79a, which shows a water tank subjected to a blast force ft . We will model the...Problem 4.80P:
The “sky crane” shown on the text cover was a novel solution to the problem of landing the 2000 lb...Problem 4.84P:
Suppose a mass in moving with a speed 1 becomes embedded in mass after striking it (Figure 4.6.1)....Problem 4.85P:
Consider the system shown in Figure 4.6.3. Suppose that the mass m moving with a speed 1 rebounds...Problem 4.87P:
Figure P4.87 shows a mass m with an attached stiffness, such as that due to protective packaging....Problem 4.88P:
Figure P4.88 represents a drop forging process. The anvil mass is m1=1000 kg, and the hammer mass is...Problem 4.89P:
Refer to Figure P4.89. A mass m drops from a height h and hits and sticks to a simply supported beam...Problem 4.91P:
(a) Obtain the equations of motion of the system shown in Figure P4.25. (b) Suppose the inertias are...Problem 4.92P:
Refer to part (a) of Problem 4.90. Use MATLAB to obtain the transfer functions X1s/Fs and X2s/Fs ....Problem 4.93P:
Refer to Problem 4.91. Use MATLAB to obtain the transfer functions 1s/T2s and 2s/T2s for the values...Browse All Chapters of This Textbook
Chapter 1 - IntroductionChapter 2 - Dynamic Response And The Laplace Transform MethodChapter 3 - Modeling Of Rigid-body Mechanical SystemsChapter 4 - Spring And Damper Elements In Mechanical SystemsChapter 5 - Block Diagrams, State-variable Models, And Simulation MethodsChapter 6 - Electrical And Electromechanical SystemsChapter 7 - Fluid And Thermal SystemsChapter 8 - System Analysis In The Time DomainChapter 9 - System Analysis In The Frequency DomainChapter 10 - Introduction To Feedback Control Systems
Book Details
System Dynamicsincludes the strongest treatment of computational software and system simulation of any available text, with its early introduction of MATLAB� and Simulink�. The text's extensive coverage also includes discussion of the root locus and frequency response plots, among other methods for assessing system behavior in the time and frequency domains as well as topics such as function discovery, parameter estimation, and system identification techniques, motor performance evaluation, and system dynamics in everyday life.
Sample Solutions for this Textbook
We offer sample solutions for System Dynamics homework problems. See examples below:
Concept Used: 1 slug = 32.2 pounds. 32.2 lb = 143 N. 1 lb = 0.453592 kg. Calculation: The weight of...Given Information: Function f(θ)=sinθ Consider the following data. Function f(θ)=sinθ Angles, θ=π4...Given Information: Data is given by: x:2530354045y:02505007501000. Calculation: From the given data...Given: Half-life of carbon -14 is 5500 years Concept Used: Fraction of carbon -14 remaining time at...Given: yy¨+5y˙+y=0. Concept Used: An ordinary differential for y=y(t) is said to be linear if it can...Given: F(s)=6s2+9. Concept Used: Laplace transform of function f(t) is defined as...Given: F(s)=5ss2+9. Concept Used: Laplace transform of function f(t) is defined as...Given: The signal in frequency domain is given as shown below. X(s)=6s(s+4) Concept Used: The...Given: The given equation is as: x¨+8x˙+15x=30 With initial conditions as follows: x(0)=10 and...
Given: The given model equations are as: x˙=−4x+2y +f(t)and y˙=−9y−5x+g(t). Concept Used: Laplace...Given: The given model equation is as: 7x˙+5x=4g˙(t) Where, g(t)=us(t) and the initial conditions...Given: m=2,a=g, s=h and u=0 The height of the platform from the ground is 10 feet. The height of the...Given: Weight of a rear wheel = 500 lb. Weight of front wheel = 800 lb. Weight of the body = 9000...Given: Roller radius = R Inertia of roller = mR22 Mass of roller = m Weight of roller = 800N...Given: Wheel radius, R = 0.05m Mass of rod, m = 20kg Length of rod, L = 1.4m Mass of the wheel is...Given: Friction of the pivot and mass of the scale arm are neglected. Concept used: For an objects’...Given information: The number of turn in a coil is 6, the diameter of the coil is 4 in, the diameter...Write the expression for equality condition of potential energy and kinetic energy for Rayleigh’s...Given information: The mass of the block on an inclined plane is 50 kg, the angle of inclination is...Given information: The value of step function is 5000 and the equation of motion is...Given information: The damping coefficient is c and friction is negligible. The figure below shows...Figure (1) shows the free body diagram of the system. Figure-(1) Consider a point A on the system...Figure (1) shows the free body diagram of the system shown in part (a). Figure-(1) Here, the...Given: A spring with stiffness k, and a damper with damping coefficient c, are attached to a...Given: A spring with stiffness k, and a damper with damping coefficient c, are attached to a...Given: The masses are m1=20 kg and m2=60 kg The spring constant are k1=3×104 N/m and k2=6×104 N/m...Given: The given block diagram is as shown in figure (i). Concept Used: The given block diagram is...Given: The block diagram for the model with input R(s) and the output as C(s). Concept Used: The...Given: The transfer function of the system is as shown: Y(s)F(s)=s+2s2+4s+3 With given initial...Given information: The given relation between the voltage and current is, vs=Rei All resistors are...Given: The speed control system for the field-controlled motor has been given as shown in figure 1:...Given information: The given parameters for the armature-controlled motor are as follows: KT=Kb=0.05...Given: The given parameters for an armature-controlled motor are as: Kb=KT=0.2 N⋅m/A, c=5×10−4...Given: The electrical and mechanical sub-system of the speaker system is shown in figure below:...Given information: The area of the left side is 10 in2, the area of right side is 30 in2, the weight...Calculation: The figure below shows the pump curve and the line for steady-state flow. Figure-(1)...Calculation: Write the radial resistance of the pipe. Rp=ln(rori)2πkL...... (I) Here, the inner...Given information: The initial temperature of water is 120°F, the length of copper pipe is 6 ft,...Calculation: Write the expression for the rate of heat transfer in terms of total thermal...Calculation: Write the expression for the thermal capacitance of the first mass. C1=dq1dT1dq1=C1dT1...Given: The equation of motion for the rocket sled is, 6v˙=2700−24v v(0)=0 Concept Used: Use Laplace...Given information: The given model equation is as: 2x˙+x=10f(t) With initial conditions as follows:...Given: The given model equation is as: x¨+4x˙+8x=2us(t) With initial conditions as follows: x(0)=0...Given: The given model equation is as: 3x¨+21x˙+30x=f(t) With initial conditions as follows: x(0)=0...Given: The given model equation is as: 3x¨+21x˙+30x=4t With initial conditions as follows: x(0)=0...Given Information: Transfer function is given by, T(s)=Y(s)F(s)=2514s+18. Input signal is,...Given: T(s) =8s(s2+10s+100), f(t)=6sin9t. Concept Used: Using the final value theorem Calculation:...Given: The circuits are as shown below: Concept Used: Kirchhoff’s current and voltage laws are...Given: The displacement produced by the cam is given by the following figure Figure 1 Figure 2 Where...Given: To consider a Traffic light as a device A device or process is said to be in a closed loop if...Given: The proportional integral controller of the first order plant is as shown below: Where, the...Given: The proportional integral controller of first order plant is as shown below: Where, the...Given: The I controller with an internal feedback loop of first order plant is as shown below:...Given: The I controller with an internal feedback loop of first order plant is as shown below:...Given: The proportional integral controller of first order plant is as shown below: Where, the...Given: The proportional integral controller of first order plant is as shown below: Where, the...Given information: The characteristic equation is given as 3s2+12s+k=0 for k≥0. Concept Used: Root...Given: 1+G(s)H(s)=s(s+5)+K for K≥0. Concept Used: Root Locus technique. Calculation: The...Given: 1+G(s)H(s)=s(s+5)+K for K≥0. Concept Used: Root Locus technique. Calculation: The...Given: The equation is Gp(s)=4p(s2+4ζs+4)(s+p). ζ=0.5,p=1. Concept Used: Ultimate cycle technique of...Given information: The transfer function of the plant is Gp(s)=Θ(s)Φ(s)=15s2−6. For a closed loop...Given: m=0.5 kgk=500 N/mY=4 mmf=3 Hz Concept Used: Displacement transmissibility. Calculation: The...Given information: The main mass is m1. Write the expression for force of mass 1....Given information: The main mass is m1. Write the expression for force of mass 1....Given information: The stiffness of suspension 1 is 1.95×104 N/m, the stiffness of the suspension 2...
More Editions of This Book
Corresponding editions of this textbook are also available below:
System Dynamics
1st Edition
ISBN: 9780073016030
System Dynamics (mcgraw-hill Mechanical Engineering)
1st Edition
ISBN: 9780256114492
SYSTEM DYNAMICS (OPTIONAL PRINT UPGRADE)
4th Edition
ISBN: 9781264262250
SYSTEM DYNAMICS (LOOSELEAF)
4th Edition
ISBN: 9781260443981
SYSTEM DYNAMICS
4th Edition
ISBN: 9780078140051
SYSTEM DYNAMICS CONNECT
4th Edition
ISBN: 9781265781651
SYSTEM DYNAMICS CONNECT W/LL COMBO
4th Edition
ISBN: 9781265824532
SYSTEM DYNAMICS (LOOSELEAF)-W/CONNECT
4th Edition
ISBN: 9781264094042
SYSTEM DYNAMICS-CONNECT ACCESS
4th Edition
ISBN: 9781260443950
EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
System Dynamics
3rd Edition
ISBN: 9780077509125
SYSTEM DYNAMICS>LOOSELEAF<
3rd Edition
ISBN: 9781260163087
System Dynamics (Looseleaf) (Custom)
14th Edition
ISBN: 9781259114151
SYSTEM DYNAMICS CONNECT
3rd Edition
ISBN: 9781264201730
SYSTEM DYNAMICS LL+CONNECT
3rd Edition
ISBN: 9781264201891
System Dynamics
2nd Edition
ISBN: 9780071267793
System Dynamics
2nd Edition
ISBN: 9780073529271
System Dynamics
2nd Edition
ISBN: 9780077417260
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