4. A cuckoo clock pendulum consists of two pieces attached together:5. A thin rod with mass m₁ and length 7.6. A circular disk with mass m2 and radius r, centered at the midpoint of the thin rod.The pendulum is attached at one end to a fixed pivot O, as shown below, where a time-varyingtorque (t) is also applied. Note that gravity acts on the system.Instructions:a) Find the expression for the mass moment of inertia of the pendulum Izz with respect to O.b) Find an expression for the angular momentum of the pendulum with respect to O.c) Draw a free-body diagram for the system.Y₁₁(t)T(t)OXθm119m2

Answered: Image /qna-images/answer/304fd8fd-6a67-4205-a09a-019c9a1ce2d7.jpg

Answered: 4. A cuckoo clock pendulum consists of…

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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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…
Question 9: Figure 3 shows a mechanical system. The rod (with moment of inertia J) rotates about the pivot at only small rotation angles. As pictured, theta is positive clockwise. Attached is mass m, which moves positive to the right. When stationary in the position shown, all springs are undeflected. Using BOBODDY, find the mathematical model of this system assuming small rotation angle 0. Link, moment of inertia J k3 L₁ 12 5 Ꮎ wwww Figure 3: Mechanical System m k₂ b
Questions A and B
M=2kg m=2kg w=4 e=2 omega=4t please solve with angular motion
Q2
Dynamics
The radius, r, of the pulley shown in figure Q1 is 100mm and has a mass moment of inertia of I = 0.1 kg m². The mass, m, is 5kg and the spring constant is k = 135N/m. The system is released from rest with the spring unstretched. At the instant the mass has fallen 0.2m, determine the: A) Angular acceleration of the pulley. B) Tension in the rope between the mass and the pulley. www m X Figure Q1 - Mass pulley system
Vibration topic. Please help to provide solution with the problem with correct unit and answer. Will upvote to the answer. Thanks
* F2 # 3 E Problem 4. EOM Derivation Derive the equation of motion for the following system: We want to measure the spin rate w of the rotating shaft of a turbine. To do it we push a small mass m against the end of the shaft. The shaft makes friction contact with the drag cup mounted on the mass. The frictional torque is b (w). Assume that the rotational spring torque is ke and that the moment of inertia of mass m is J. J Rotating Shaft F3 @ $ 4 R b J, m Drag Cup F4 Q Search % 5 F5 T 0 Wall * A 6 F6 Y 2 * F7 & 7 PrtScn U F8 4 8 Home 6. F9 9 End F10 Po 0
Derive the governing equation of motion for the rocker-arm valve assembly shown below. Assume "small" motions. The quantity Jo is the mass moment of inertia about point O of the rocker arm of length (a + b), k is the stiffness of the linear spring that is fixed at one end, c is the damping coefficient of the linear damper, and M is the external moment imposed by the cam on the system. This moment is produced by the contact force generated by the cam at the end of the rocker arm. Jo k
3. Quarter car suspension model The figure below a model of the suspension of a car. r(t)is the position of the mass of the car from its equilibrium position while z is the profile of the road. Note that z is a function of the distance y along the road, but you need ż(t) which you can obtain from z(y) using the chain rule. The car is traveling to the right on the road at a speed v. Assume the mass of the car is 250 kg, the spring constant is 16 kN/m, and damping constant is 1000 Ns/m. (a) Derive the differential equation for the position of the car r(t). (b) If z(t) = Zoejot, determine the amplitude and the phase of the particular solution. (c) (MATLAB) If the car is travelling with constant velocity along a road with rolling hills that can be represented as a cosine function with amplitude Zo and wavelength A (wavelength is the distance between adjacent crests or adjacent troughs, determine the vertical motion of the car as a function of time. X(t) Z m 1 C Figure 1: Quarter car…

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