SYSTEM DYNAMICS LL+CONNECT
3rd Edition
ISBN: 9781264201891
Author: Palm
Publisher: MCG CUSTOM
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Chapter 3, Problem 3.17P
Derive the expression for the equivalent inertia
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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.
A mass weighing 4 pounds is attached to a spring whose spring constant is 36 lb/ft.
Find the equation of motion.
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 floor
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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- Find the axial displacement of a rod given properties L(length), A (cross sectional area), E (Modulus) impacted axially by a mass m moving with a velocity v0?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_forwardFor the double slider mechanism shown in the following figure, the crank OA rotates at a uniform speed of 100 rad/s CW. we need to find the required torque for the crank, if two forces act at sliders B and C as shown in the figure. (P = 2KN, Q = 1KN). OA = 30 cm, AB = AC = 100 cm. mB = mC = 1 Kg. Neglect other links weights. The velocity of slip of slider B in m/s2 = Answer 1 Choose... The velocity of slip of slider C in m/s2 = Answer 2 Choose... The acceleration of slip of slider B in m/s2 = Answer 3 Choose... The acceleration of slip of slider C in m/s2 = Answer 4 Choose... The magnitude of required torque for the crank in N.m = Answer 5 Choose...arrow_forward
- If 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_forwardA 20 kg skip attached to a steel rope on a crane is used to hoist bricks from the ground to the top of a construction site. The steel rope is wound onto a lifting drum with a diameter of 700 mm which rotates. The lifting drum is situated on the top floor. Calculate the torque (in N.m) on the lifting drum, to lift 20 bricks weighing 150 kg, ignoring the weight of the steel rope.arrow_forwardIn the pulley system shown in Figure P3.22, assume that the cable is massless and inextensible, and assume that the pulley masses are negligible. The force f is a known function of time. Obtain the expression for the natural frequency.arrow_forward
- 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?arrow_forwardYou are using a lightweight rope to pull a sled along level ground. The sled weighs 435 N, the coefficient of kinetic friction between the sled and the ground is 0.200, the rope is at an angle of 12∘ above the horizontal, and you pull on the rope with a force of 115 N. Find the normal force that the ground exerts on the sled. Find the acceleration of the sled. Is the sled speeding up or slowing down?arrow_forward1. The blades of a rotary lawnmower are 30cm long and rotate at 315rad/s. Find the linear speed of the blade tips and their angular speed in rpm? 2. A rotating platform is to be used to test aircraft equipment under accelerations of 6 grams. If the equipment is 50cm from the axis, what angular speed is needed?arrow_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_forward'A model for the elbow joint models the bicep muscle connecting to the horizontal forearm by a vertical tendon 4cm from the elbow joint. A mass m is held in the hand 30cm from the elbow joint. If the maximum tension that can be exerted by the tendon before injury occurs is 2250N, find the maximum mass that can be held in this way.' Im stuck on this questionarrow_forwardA rock is thrown horizontally off a 100 m high-rise building as shown in Figure Q4(a). It lands 95 m away. At what speed was it thrown?arrow_forward
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