SYSTEM DYNAMICS LL+CONNECT
3rd Edition
ISBN: 9781264201891
Author: Palm
Publisher: MCG CUSTOM
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Chapter 3, Problem 3.31P
Assume the cylinder in Figure P3.31 rolls without slipping. Neglect the mass of the pulleys and derive the equation of motion of the system in terms of the displacement x.
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You pull on a crate using a rope as image, except the rope is at an angle of 20.0 ∘ above the horizontal. The weight of the crate is 325 N, and the coefficient of kinetic friction between the crate and the floor is 0.230. What must be the tension in the rope to make the crate move at a constant velocity? What is the normal force that the floor exerts on the crate?
MECHANICAL 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.
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Chapter 3 Solutions
SYSTEM DYNAMICS LL+CONNECT
Ch. 3 - Prob. 3.1PCh. 3 - A baseball is thrown horizontally from the...Ch. 3 - For the mass shown in Figure 3.1.3b. m=10 kg, =25...Ch. 3 - A particle of mass m=19 kg slides down a...Ch. 3 - A particle of mass m slides down a frictionless...Ch. 3 - A radar tracks the flight of a projectile (see...Ch. 3 - Table 3.2.1 gives the inertia IO for a point mass...Ch. 3 - A motor supplies a moment M to the pulley of...Ch. 3 - Figure P3.9 shows an inverted pendulum. Obtain the...Ch. 3 - The two masses shown in Figure P3.10 are released...
Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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- In the figure below Atwood’s machine is drawn - two masses and hanging over a massive pulley of rotational inertia and radius , connected by a massless unstretchable string. The string rolls on the pulley without slipping.a) Find the acceleration of the system and the tensions in the string on both sides of the pulley in terms of in terms of given variables.b) Why are the rope tensions on two sides of the pulley not the same? Explain it physically.c) Suppose mass and the system is released from rest with the masses at equal heights. When mass has descended a distance , find the velocity of each mass and the angular velocity of the pulley.[4***] A string is rolled around a cylinder( kg) as shown in figure. A person pulls on the string, causing the cylinder to roll without slipping along the floorarrow_forwardConsider the mass spring system shown in the figure below. The system is subject to a time dependent forcearrow_forwardFigure Q1 shows a uniform plank, rests upon a horizontal bench with one end of the bar projecting over the sharp edge of the bench, the bar being at right angles to this edge. The plank is pulled out of horizontally until the centre of gravity overhangs the edge by a distance a, and is then released. The plank rotates about the edge and then slides down.arrow_forward
- Find the differential equations for the motion of a pendulum in that its mass m is connected to a flexible helical spring (constant of stiffness K and length l. ). Assume that the movement takes place in a vertical plane.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, (i) With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A.arrow_forwardA uniform wheel of 60 cm diameter and weighing 1000N rest against a rectangular block 15 cm high lying on a horizontal plane as shown in the figure. It is to be pulled over the block by a horizontal force p applied to the end of a string wound round the circumference of the wheel. Find the force P when the wheel is just about to roll over the block ?arrow_forward
- In the mechanical system in the figure, a rigid rod is bedded at point P and has mass m at its end. can rotate vertically. At the other end of the rod, a spring (k) and a damper (c) are attached. Draw the Free-Body Diagram of the system, obtain the Equation of Motion (the vertical position of the ball We assume that the displacement x is very small and the bar is massless).arrow_forwardIf a disk (radius R) is subjected to two tangential forces of equal value and accelerates initially, but then reaches a constant angular velocity how would you represent the torque acting upon the center of the desk?arrow_forwardcomo se resuelve esta ecuacion for each of the rotational mechanical systems shown in figure write, but do not solve, the equations of motionarrow_forward
- Figure P3.40 illustrates a pendulum with a base that moves horizontally. Thisis a simple model of an overhead crane carrying a suspended load with cables.The load mass is m, the cable length is L, and the base acceleration is a(t).Assuming that the cable acts like a rigid rod, derive the equation of motion interms of ? with a(t) as the input.arrow_forwardAn electric motor is accelerating a 250 kg load with acceleration of 1.2 m/s? througha gear box as shown Figure Q1(b). The rope that carries the load and spiral spring are encircled on a pulley with diameter 1.2m. Gear box ratio is 0. 1 and gear box efficiency is 100%, while gear box equivalent moment inertia is 5.55 km?. Neglect friction effect in this drive system and assume spiral spring force is X newtonCalculate the torque of the motor needed to bring up the load with acceleration1.2 m/s?.arrow_forwardPART OF MECHANICAL VIBRATIONS SUBJECT USE VIRTUAL WORK The uniform bar shown in Fig. P3.6 has mass m, length l, and mass moment of inertia 1 about its mass center. The bar is supported by two springs kı and k2, as shown in the figure. Obtain the differential equation of motion and determine the natural frequency of the system in the case of small oscillations.arrow_forward
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