2.19 Figure P2.19 shows a mechanical system that consists of a pulley on a rigid shaft. The pulley has moment of inertia J and radius r. An external torque Tin is applied directly to the pulley. Derive the mathematical model. Input torque, Tin Figure P2.19 Pulley, J )) Po m Viscous friction in bearings, b twin

2.19 Figure P2.19 shows a mechanical system that consists of a pulley on a rigid shaft. The pulley has moment of inertia J and radius r. An external torque Tin is applied directly to the pulley. Derive the mathematical model. Input torque, Tin Figure P2.19 Pulley, J )) Po m Viscous friction in bearings, b twin

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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2.16 A two-mass translational mechanical system has the following mathematical model: mi + b₁1+k₁(x1 - x₂) = fa(t) m2 2 + b₂2+k₁(x₂-x₁) + k₂x2 = 0 The displacements x, and x₂ are measured from their respective equilibrium positions. An external force fa(t) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacements on your sketch. Sketch the FBDs for each mass and verify the system model by applying Newton's laws.
2.1 Figure P2.1 shows a single-mass translational mechanical system. Both springs are undeflected when z = 0 and fa(t) = o. Derive the mathematical model of the mechanical system. Figure P2.1 fa(t) www. Z m k₂ www
igure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y 0, and the springs are in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. DE only 225 Your tasks: X k 0 3k a F a M y A Derive an equation of motion for the system in terms of the angular displacement 0, and its derivatives (you should not have y or its derivatives in this equation.) B Derive an equation of motion for the system in terms of the displacement y, and its derivatives (you should not have or its derivatives in this equation. C Assuming there is no external actuator force F acting on the system, write down the total energy H of the system in terms of 0,0 and element constants. Derive an expression for the time derivative H of the total energy. D Transform the equation from part B, which is in y, to another…
3.25 The coefficient of friction between the disk and the surface in Figure P3.24 is u. What is the largest initial velocity of the mass center that can be imparted such that the disk rolls without slip for its entire motion? Thin disk of mass m. no slip FIGURE P3.24 Given: u, m, k, r
A 50.0N weight uniform 4 metre long beam is hanging from a cord held out at a 30° angle as shown. And unknown weight not shown in the diagram is also hanging 1 m from the X on the diagram. A) The tension in the cord is measured with a spring balance and found to be 130 N. find the counter clockwise torque from the cord about the X shown in the diagram. B) balance torques to find the torque from the unknown weight that is not shown in the diagram Hint: add the unknown weight to the diagram and do not forget to include the weight of the beam in your calculation
0.5 m, k = 500 N/m, and k = 40 N.m/rad, In the system shown, m = 10 kg, r = 0.3 m, Ko where ko is the radius of gyration of the pulley about point 0. There is no slippage between the cord and the pulley. Replace the system with an equivalent { a) torsional spring and mass moment of inertia at point 0, and b) translational mass and spring at point A. т, Ко kt А k m ww
For this problem, take a look at Figure 2 below. A disk with uniformly distributed mass m, radius R, and center of mass at point O is connected to a combination of springs at point P, which are then connected to a fixed wall. The disk rolls without slipping at point Q along an inclined plane that is at an angle a from the horizontal. Gravity acts in the vertical direction (towards the bottom of the page). ₁ is the linear coordinate of the point O along the inclined plane. The positive direction of ₁ is as shown. When the springs are undeflected, *₁ = 0. An angle , about the instant center of rotation, is shown. You may assume that the motion (and therefore angle ) is small. puny m Massless structure between springs R Figure 2: System schematic. Your tasks: A Draw the FBD for the disk. Don't forget the forces at point Q B Derive the equation of motion with as the dynamic variable. Be sure to put it in input-output standard form (inputs and constant forces on the right, things related to…
The pulley shown in Figure P1.27 is connected to abracket with a circular pin of diameter d = 6 mm. Each vertical sideof the bracket has a width b = 25 mm and a thickness t = 4 mm. Ifthe pulley belt tension is P = 570 N, what is the average bearingstress produced in the bracket by the pin?
4.35 Find the response of the mass shown in Fig. 4.56 under the force F(1) = Foe using convo- lution integral. Data: k, = 1000 N/m, k, = 500 N/m, r = 5 cm, m = 10 kg, , = 1 kg-m, Fo = 50 N. %3D Pulley, mass moment of inertia o
1. A spring mass system serving as a shock absorber under a car's suspension, supports the M 1000 kg mass of the car. For this shock absorber, k = 1 × 10°N /m and c = 2 × 10° N s/m. The car drives over a corrugated road with force %3| F = 2× 10° sin(@t) N . Use your notes to model the second order differential equation suited to this application. Simplify the equation with the coefficient of x'" as one. Solve x (the general solution) in terms of w using the complimentary and particular solution method. In determining the coefficients of your particular solution, it will be required that you assume w – 1z w or 1 – o z -w. Do not use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w. You must indicate in your solution: 1. The simplified differential equation in terms of the displacement x you will be solving 2. The m equation and complimentary solution xe 3. The choice for the particular solution and the actual particular solution x,…
a) Let's start with a simplified model where both M, and M₂ are applied perpendicular to the moment arm. The moment arm lengths are d₁ = 3 cm, d₂ 15 cm, and d3 = 34 cm. M₁ M₂ da W Calculate the ratio of the mechanical advantage of the brachioradialis(M₂) to the mechanical advantage of the biceps(M₁). Ratio of Mechanical Advantage MA2 -) = 5 MA1
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