Sphere, mass mFind the equivalent stiffness and mass of the systemshown in the figure, then find the natural frequency.No slipBell crank lever,mass moment ofinertia Jo90°4k₁m00000x(1)

The equivalent stiffness of the system can be determined by considering the stiffness of the…

Answered: Sphere, mass m Find the equivalent…

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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Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128
Question 1 A sketch of a valve and rocker arm system for an internal combustion engine is give in below figure. Model the system as a pendulum attached to a spring and a mass. Determine the equations of motion and calculate the natural frequency in rad/s. The mass moment of inertia of the rocker arm about its pivot point j=0.46, the stiffness of the valve springspring k=420 , the distance from pivot to spring I= 0.98 m, and the mass of the valve m=3.2 kg. Ignore the mass of the spring and the oil effect. Rocker arm Follower k Valve spring LOil Cam m Valve
F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.
Q4-6 please
A sketch of a valve and rocker arm system for an internal combustion engine is give in Figure. Model the system as a pendulum attached to a spring and a mass and assume the oil provides viscous damping in the range of 3= 0.01. Determine the equations of motion and calculate an expression for the natural frequency and the damped natural frequency. Here J is the rotational inertia of the rocker arm about its pivot point, k is the stiffness of the valve spring and m is the mass of the valve and stem. Ignore the mass of the spring. Hint: apply Lagrange equation method Rocker arm 0 J k m Solution: Ꮎ Follower k Valve spring Oil Cam m Valve l x
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Q3:-Find the natural frequency for the system shown (assume massless links) by using Energy Method. us kz a a
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* 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

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Sphere, mass m Find the equivalent stiffness and mass of the system shown in the figure, then find the natural frequency. No slip Bell crank lever, mass moment of inertia Jo 90° 4 k₁ m 00000 x(1)