Concept explainers
Figure P4.88 represents a drop forging process. The anvil mass is
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
System Dynamics
- A mass weighing 16 pounds stretches a spring 83 feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.)arrow_forwardQ3/ For the system shown in figure if the damping ratio is 0.3 derive the equation of motion using Newton's second law and find: a- The natural frequency. b- The damping constant. c- The ratio of any consecutive cycles. k=2 x 10 N/m m = 4.2 kg 10 cm 40 cm 60 cm ITTTIarrow_forward4.8. A damped single degree of freedom mass-spring system has a mass m = 3 kg, a spring stiffness k = 2700 N/m, and a damping coefficient c = 18 N-s/m. The mass is subjected to a harmonic force which has an amplitude Fo = 20N and a frequency wf = 15 rad/s. The initial conditions are xo = 4 cm, and to = 0. Determine the displacement, velocity, and acceleration of the mass after time t = 0.5 s.arrow_forward
- The slender bar of Figure 3.9(a) has a mass of 31 kg and a length of 2.6 m. A 50 N force is statically applied to the bar at P then removed. The ensuing oscillations of Pare moni- tored, and the acceleration data is shown in Figure 3.9(b) where the time scale is calibrated but the acceleration scale is not. (a) Use the data to find the spring stiffness k and the damping cocfficient c. (b) Calibrate the acceleration scale.arrow_forwardSuppose a mass-spring system has spring constant 712 N/m and mass 4.4 kg. The mass is displaced in the negative x-direction by 0.22 m and set in motion at 2.55 m/s in the positive x-direction. Calculate the phase shift as a positive angle in radians, assuming a cosine solution.arrow_forwardYou have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system. Assuming the usual units you may suppose the mass of the coal m=1, k=3, and the damping constant b = 1. Write down an ODE that models the behavior of this system. If you stretch the spring 1 meter and let it go with no initial velocity, determine the position of the mass after t seconds. At t=4 seconds you whack the mass with a giant candy cane imparting 5 units of impulse. Keeping the same system and the same initial conditions, now determine the position of the mass aftert seconds. PLEASE ANSWER THE LAST QUESTION. (At t=4 seconds you whack the mass with a giant candy cane imparting 5 units of impulse. Keeping the same system and the same initial conditions, now determine the position of the mass after t seconds.)arrow_forward
- 4.4. A spring-mass system is subjected to a harmonic force which has an amplitude 30N and frequency 20 rad/s. The system has mass m = 5 kg, and stiffness coefficient k= 2 x 10° N/m. The initial conditions are such that xo = 0, io = 2 m/s. Determine the displacement, velocity, and acceleration of the mass after 0.5, 1, 1.5 s.arrow_forwardA 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_forward8 kg hinged at point C. Figure Q3(b) shows a uniform bar AB of mass = Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle 0 = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A. (i) (ii) Determine the period of vibration. (iii) Determine the maximum velocity and acceleration at point A k wive A 250 mm • G 40 mm Вarrow_forward
- A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is released from a point 10 cm below its equilibrium position with an upward velocity of 15 cm/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to twelve times the instantaneous velocity. Find the position function (the equation of motion) if the mass is driven by an external force f(t)=40cos(5t).arrow_forward2. The base of a spring-mass system, with Coulomb damping, is connected to the slider-crank mechanism shown in Figure (P3.2). Determine the response (natural frequency, damping ratio) of the system for a coefficient of friction between the mass and the surface by approximating the motion y(t) as a series of harmonic functions for and o = 100 rad/s. Discuss the limitations of your solution. m = 1 kg, k = 100 N/m, r = 10 cm, 1= 1 m, µ = 0.1, k 0 = ot m www Fig. P3.2 oriodicarrow_forwardA 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from x = 0.0 cm with a velocity of 0.370 m/s to the left. Find the followingA. Time periodB. Total mechanical energy of the massC. AmplitudeD. Phase constant of motion. Discuss the two possible values of phase constant you get and explain how you arrived at the correct answer. Write the equation of motion.E. Maximum acceleration of the mass. (Acceleration is maximum when it ispositive). How long after the release does the maximum acceleration occur?F. Draw the position-time graph for one cycle of motion.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY