System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Question
Chapter 4, Problem 4.62P
To determine
The equation of motion.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A 2D incompressible flow has velocitycomponents u= X^2 - 2y^2 and v=aX^b y^c
，where a, b, and c are numbers.
Find the values of a, b, and c
Find the stream function
Please can you assist with the attached question please?
(a) Find a second-order homogeneous linear ODE for which the given functions are
solutions. (b) Show linear independence by the Wronskian. (c) Solve the initial value
problem.
a. cos(5x), sin(5x), y(0) = 3, y'(0) = −5
b. e-2.5x cos(0.3x), e-2.5x sin(0.3x), y(0) = 3, y'(0) = -7.5
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
Similar questions
- Solve the IVP. a. y" 16y 17e* ; = y(0) = 6, y'(0) = -2 b. (D² + 41)y = sin(t) + ½ sin(3t) + sin(t) ; y(0) = 0, y'(0) : = 35 31arrow_forwardFind the general solution. a. y' 5y = 3ex - 2x + 1 - b. y" +4y' + 4y = e¯*cos(x) c. (D² + I)y = cos(wt), w² # 1arrow_forwardhandwritten solutions, please!!arrow_forward
- > Homework 4 - Spring 2025.pdf Spring 2025.pdf k 4 - Spring 2025.pdf (447 KB) Due: Thursday, February 27 Page 1 > of 2 ZOOM 1. A simply supported shaft is shown in Figure 1 with wo = 25 N/cm and M = 20 N cm. Use singularity functions to determine the reactions at the supports. Assume EI = 1000 kN cm². M Wo 0 10 20 30 40 50 60 70 80 90 100 110 cm Figure 1 - Problem 1 2. A support hook was formed from a rectangular bar. Find the stresses at the inner and outer surfaces at sections just above and just below O-B. 210 mmarrow_forwardA distillation column with a total condenser and a partial reboiler is separating ethanol andwater at 1.0 atm. Feed is 0.32 mol fraction ethanol and it enters as a saturated liquid at 100mol/s on the optimum plate. The distillate product is a saturated liquid with 80 mol% ethanol.The condenser removes 5615 kW. The bottoms product is 0.05 mol fraction ethanol. AssumeCMO is valid.(a) Find the number of equilibrium stages for this separation. [6 + PR](b) Find how much larger the actual reflux ratio, R, used is than Rmin, i.e. R/Rmin. [3]Note: the heats of vaporization of ethanol and water are λe = 38.58 and λw = 40.645 arrow_forwardWe have a feed that is a binary mixture of methanol and water (60.0 mol% methanol) that issent to a system of two flash drums hooked together. The vapor from the first drum is cooled,which partially condenses the vapor, and then is fed to the second flash drum. Both drumsoperate at 1.0 atm and are adiabatic. The feed to the first drum is 1000 kmol/hr. We desire aliquid product from the first drum that is 35.0 mol% methanol. The second drum operates at afraction vaporized of (V/F)2 = 0.25.(a) Find the liquid flow rate leaving the first flash drum, L1 (kmol/hr). [286 kmol/hr](b) Find the vapor composition leaving the second flash drum, y2. [0.85]arrow_forward
- = The steel curved bar shown has rectangular cross-section with a radial height h = 6 mm and thickness b = 4mm. The radius of the centroidal axis is R = 80 mm. A force P = 10 N is applied as shown. Assume the steel modulus of 207,000 MPa and G = 79.3(103) MPa, repectively. elasticity and shear modulus E = Find the vertical deflection at point B. Use Castigliano's method for a curved flexural member and since R/h > 10, neglect the effect of shear and axial load, thereby assuming that deflection is due to merely the bending moment. Note the inner and outer radii of the curves bar are: r = 80 + ½ (6) = 83 mm, r₁ = 80 − ½ (6) = 77 mm 2 2 Sπ/2 sin² 0 d = √π/² cos² 0 d0 = Π 0 4 大 C R B Parrow_forwardThe steel eyebolt shown in the figure is loaded with a force F = 75 lb. The eyebolt is formed from round wire of diameter d = 0.25 in to a radius R₁ = 0.50 in in the eye and at the shank. Estimate the stresses at the inner and outer surfaces at section A-A. Notice at the section A-A: r₁ = 0.5 in, ro = 0.75 in rc = 0.5 + 0.125 = 0.625 in Ri 200 F FAarrow_forwardI have the fallowing question and solution from a reeds naval arc book. Im just confused as to where this answer came from and the formulas used. Wondering if i could have this answer/ solution broken down and explained in detail. A ship of 7000 tonne displacement has a waterplane areaof 1500 m2. In passing from sea water into river water of1005 kg/m3 there is an increase in draught of 10 cm. Find the Idensity of the sea water. picture of the "answer" is attachedarrow_forward
- Problem A2 long steel tube has a rectangular cross-section with outer dimensions of 20 x 20 mm and a uniform wall thickness of 2. The tube is twisted along its length with torque, T. The tube material is 1045 CD steel with shear yield strength of S,, =315 MPa. Assume shear modulus, G = 79.3GPa. (a) Estimate the maximum torque that can be applied without yielding (b) Estimate the torque required to produce 5 degrees total angle of twist over the length of the tube. (c) What is the maximum torque that can be applied without yielding, if a solid rectangular shaft with dimensions of 20 x 20 is used? You may use the exact solution.arrow_forwardA simply supported beam is loaded as shown. Considering symmetry, the reactions at supports A and B are R₁ = R₂ = wa 2 Using the singularity method, determine the shear force V along the length of the beam as a function of distance x from the support A. A B Ir. 2a За W C R₁₂ x 2. Using the singularity method, determine the bending M along the length of the beam as a function of distance x, from the support A. 3. Using the singularity method, determine the beam slope and deflection along the length of the beam as a function of the distance x, from the support A. Assume the material modulus of elasticity, E and the moment of inertia of the beam cross-section, I are given.arrow_forwardA steel tube, 2 m long, has a rectangular cross-section with outer dimensions of 20 × 30 mm and a uniform wall thickness of 1 mm. The tube is twisted along its length with torque, T. The tube material is 1018 CD steel with shear yield strength of Ssy =185 MPa. Assume shear modulus, G = 79.3GPa. (a) Estimate the maximum torque that can be applied without yielding.- (b) Estimate the torque required to produce 3 degrees total angle of twist over the length of the tube. (c) What is the maximum torque that can be applied without yielding, if a solid rectangular shaft with dimensions of 20 x 30 mm is used? You may use the exact solution: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