## Solutions for System Dynamics

Problem 1.2P:

Folklore has it that Sir Isaac Newton formulated the law of gravitation supposedly after being hit...Problem 1.5P:

How long is a 100-meter dash in feet?Problem 1.6P:

Convert 50 feet per second to miles per hour.Problem 1.7P:

The speed limit in some countries is 100 kilometers per hour. I-low fast is that in miles per hour?Problem 1.9P:

Convert the temperature of 70°F to °C.Problem 1.10P:

Convert 30°C to °F.Problem 1.11P:

A particular motor rotates at 3000 revolutions per minute (rpm). What is its speed in rad/sec. and...Problem 1.12P:

The displacement of a certain object is described by yt=23 sin 5t , where t is measured in seconds....Problem 1.14P:

The displacement in meters of a certain vibrating mass is described by xt=0.005 sin 6t . What is the...Problem 1.15P:

The distance a spring stretches from its “free length” is a function of how much tension is applied...Problem 1.16P:

The following “small angle” approximation for the sine is used in many engineering applications to...Problem 1.18P:

Obtain two linear approximations of the function f=cos , one valid near =/3 rad and the other valid...Problem 1.20P:

Obtain two linear approximations of the function fr=r2 , one valid near r=5 and the other valid near...Problem 1.21P:

Obtain a linear approximation of the function fh=h , valid near h=16 . Noting that fh0 . what is the...Problem 1.22P:

The flow rate f in m3/s of water through a particular pipe, as a function of the pressure drop p...Problem 1.24P:

The population data for a certain country are given here....Problem 1.26P:

Quenching is the process of immersing a hot metal object in a bath for a specified time to improve...Problem 1.27P:

The useful life of a machine bearing depends on its operating temperature, as shown by the following...Problem 1.28P:

1.28 A certain electric circuit has a resistor and a capacitor. The capacitor is initially charged...Problem 1.29P:

1.29 Water (of volume 425 ml) in a glass measuring cup was allowed to cool after being heated to...# 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 Dynamics*includes the strongest treatment of computational software and system simulation of any available text, with its early introduction of MATLABï¿½ and Simulinkï¿½. 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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