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
- (c) The spring-damper-mass system shown in Figure Q3(c) is at rest when strict by a hammer with an initial velocity of 0.4 m/s causing the mass to move upwards. Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient of viscous damping c = 0.6 Ns/m. (i) Determine the damped frequency of the spring-damper-mass system.arrow_forwardFigure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.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 θ = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A.arrow_forwardConsidering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.arrow_forward
- PART OF MECHANICAL VIBRATIONS Derive the differential equation of motion of the inverted pendulum shownin Fig. P3.8. Let m = 0.5 kg, l = 0.5 m, a = 0.2 m, and k = 3000 N/m. Determine the damping coefficient c if: (a) the system is underdamped withξ = 0.09, (b) the system is critically damped; and (c) the system is over-damped with ξ = 1.2. In these three cases determine the angular displacementand velocity after 0.4 s if the system has zero initial velocity and initialdisplacement of 4◦ counterclockwisearrow_forwardquestion 2 A mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ).arrow_forwardFigure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.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 θ = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A. p.s. This question was previously answered but because the solution images were unable to view I need to re-ask this questionarrow_forward
- A weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping force is 4 dy/dt Newtons. The weight is moved 2 meters above its equilibrium position and is started in motion with a velocity of 1 meter/sec. upward. Find the equation of motion for the weight. (There is no external force).arrow_forwardFigure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and thestiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angleθ = 3.5 degree and released,(i) With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. (ii) Determine the period of vibration. (iii) Determine the maximum velocity and acceleration at point A.arrow_forward(a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its equilibrium position and allowed to vibrate. Show that the motion is simple harmonic. (b) A vertical helical spring having a stiffness of 1540 N/m is clamped at its upper end and carries a mass of 20 kg attached to the lower end. The mass is displaced vertically through a distance of 120 mm and released. Find : 1. Frequency of oscillation ; 2. Maximum velocity reached ; 3. Maximum acceleration; and 4. Maximum value of the inertia force on the mass. (c) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dashpot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the…arrow_forward
- The 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_forwardThe system shown in Fig. P3.1 consists of a mass m and a massless rod of length l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equation of motion assuming small oscillations. Determine the natural frequency of the system.arrow_forwardA mass weighing 40 N stretches a spring 0.1 m. The spring–the mass system resides in a medium with a damping constant of 32N-s m. If the mass is released from its equilibrium position witha velocity of 0.1 m/ s in the downward direction, find the time required for the mass to return to its equilibrium position for thefirst timearrow_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