4.21. Assuming small angular oscillations, derive the differential equation ofmotion of the system shown in Fig. P4.6 where the rod is assumed to beuniform and slender. The mass and length of the rod are assumed to be mand 1, respectively.Problems175y = Y, sin w,tFig. P4.6

given; ⇒lenth of rod =l⇒mass of rod =m⇒weight of rod(w)=mg

Answered: 4.21. Assuming small angular…

Elements Of Electromagnetics

7th Edition

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Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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PART 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.
Fig. P4.6 4.22. Derive the differential equation of motion of the simple vehicle model shown in Fig. P4.7. The vehicle is assumed to travel over the rough surface with a constant vehicle speed v. Obtain also the steady state response of the vehicle. For this system, let m = 10kg, k = 4 x 103 N/m, c = 150N · s/m, i = 2 m, and the amplitude Yo = 0.1 m. Determine the maximum vertical displacement of the mass and the corresponding vehicle speed. Determine also the maximum dynamic force transmitted to the mass at the resonant speed. m 2πη y = Y, sin y Fig. P4.7
P3. The peak amplitude of a mass-spring-damper system, under a harmonic excitation, is observed to be 1 cm. The undamped natural frequency of the system is 5 Hz, and the static deflection of the mass under the maximum force is 0.5 cm. Now, instead of a harmonic excitation, a sudden impulse of 10 N.s is applied. Determine the response of the system. 4 z 0.5 cm
Please do not copy any answers already posted, they are incorrect.
A cubical block of wood 15cm on an edge and weighing 20N floats in water (9810) if it is depressed so that its upper face lies in the water surface and is then released, find the equation of motion and the period of vibration. Neglect resistance.
4.38–4.42 Determine the amplitude of steady-state vibration for the systems shown in Figures P4.38 through P4.42. Use the indicated generalized coordinate.
A block of mass m = 400 g, is attached to a horizontal spring and set in simple harmonic motion as shown. At what point(s) in the motion is the velocity of the block at its maximum? ww X = -A O a. x = 0, and x = -A O b. x=0, x= -A, and x = -A O e. O c. O d. x = 0 x = -A, and x = +A . x = 0, and x = +A m x = 0 X = +A
3.35. Obtain the differential equations of motion of the vehicle system model shown in Fig. P3.13. Assume small angular oscillations. m, 1,1 4₁ Fig. P3.13 m₁
Find the equation of motion using the Lagrangian method?
P4.7 For the scaled mechanism shown in figure P4.7, determine (a) the acceleration of point B (b) the sliding acceleration of point A2 with respect to point A4 use a complex numbers approach
Q.1 The system shown below consists of a block of mass m and a cylinder of mass 2m. The block and the cylinder are joined by pulley arrangement as show. The coordinates x and y are dependent in which x = 2y. Use m= 2 kg. The angle 0 is any value between 0 and 90°. If the cylinder is pushed downward 20 mm and released a) find the subsequent response of the block, x(1) b) find the displacement and velocity of the block at t = 1 s. The specific value of k is given in separate excel sheet. K=1985 2m IT, x = 2y
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

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4.21. Assuming small angular oscillations, derive the differential equation of motion of the system shown in Fig. P4.6 where the rod is assumed to be uniform and slender. The mass and length of the rod are assumed to be m and I, respectively. Problems 175 y = Y,sin @,t