Figure P4.49 shows a winch supported by a cantilever beam at the stern of a ship. The mass of the winch is
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Chapter 4 Solutions
SYSTEM DYNAMICS LL+CONNECT
- For the mechanical system shown below, find the equation of motions and the system matrix. Where (x = X ewt)arrow_forwardFor each of the systems shown in Figure P4.52, the input is the force f andthe outputs are the displacements x1 and x2 of the masses. The equilibriumpositions with f = 0 correspond to x1 = x2 = 0. Neglect any friction betweenthe masses and the surface. Derive the equations of motion of the systems.arrow_forwardA uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the horizontal as shown below. To answer the questions below, find algebraic expressions for the tension in the cable, the angular acceleration of the beam, should the cable break, and the resulting angular velocity as the beam falls through the vertical position. A. If L = 2.4 m, M = 5 kg, and phi = 45o, then what is the tension in the cable? B. If the cable snaps, what is the angular acceleration about the pivot point? C. What is the angular velocity of the falling beam, just as it hits the wall?arrow_forward
- Q7/ A ball of mass 0.4 kg is thrown against a brick wall. When it strikes the wall it is moving horizontally to the left at 30 m/sec ,and it rebounds horizontally to the right at 20 m/sec. find the impulse of the force exerted on the wall ?arrow_forwardMECHANICAL VIBRATIONS The system shown in Fig. P3.3 consists of a uniform rod which has length 1, mass m, and mass moment of inertia about its mass center 1. The rod is supported by two springs which have stiffness coefficients ky and k2, as shown in the figure. Determine the system differential equation of motion for small oscillations. Determine also the system natural frequency.arrow_forwardConsider the mass spring system shown in the figure below. The system is subject to a time dependent forcearrow_forward
- Q6/ A car travelling at speed of 300 m/sec strikes a stone of mass 0.5 kg and 20 cm in size .Estimate Impulse of the force by the stone on the car? Q7/ A ball of mass 0.4 kg is thrown against a brick wall. When it strikes the wall it is moving horizontally to the left at 30 m/sec ,and it rebounds horizontally to the right at 20 m/sec. find the impulse of the force exerted on the wall ?arrow_forwardSubject: Dynamics of Rigid Bodiesarrow_forwardA mass weighing 4 pounds is attached to a spring whose spring constant is 36 lb/ft. Find the equation of motion.arrow_forward
- For the rotational system shown in the figure, write the equations of motion from which the transfer function, G(s) = θ1(s)/T(s), can be found.arrow_forwardA simple pendulum of length L is set to oscillate in simple harmonic motion. The bob gravitational potential energy is zero at its lowest vertical point. When the bob's height is at half its maximum, h = hmax/2, then its velocity is:arrow_forwardAn elevator weighing 2,000 lb attain an upward velocity of 16 ft/sec in 4 seconds with uniform acceleration. What is the tension in the supporting cables?arrow_forward
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