0(+) 31 0 The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small oscillations, find the equations of motion of the two – degree – of – freedom system in terms of the given parameters (k, m,r), and show them in the matrix form. The system is in the static equilibrium position at the instant given. S.E.P. 4m 2k 5k Зт www ww

0(+) 31 0 The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small oscillations, find the equations of motion of the two – degree – of – freedom system in terms of the given parameters (k, m,r), and show them in the matrix form. The system is in the static equilibrium position at the instant given. S.E.P. 4m 2k 5k Зт www ww

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

See similar textbooks

Similar questions

A mass of a 2 slug, when attached to a spring, causes an elongation of 2 ft in this spring and then comes to rest in the equilibrium position. Starting at t = 0 an external force equal to f(t) = 8 (sin (4t)) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force equal to 8 times the instantaneous velocity.
The system shown consists of a mass m and a massless rod oflength l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equationof motion assuming small oscillations. Determine the natural frequency of thesystem.
Find the period and make a graph of "xv/s t", of a mass-spring system with elastic constant K=8 Kg/s² and m=2 Kg, which moves from its equilibrium position ma, distance d = 0.5m . Make a graph of damped and undamped.
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t= 0, an external force equal to f (t)= e^(-t)sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force numerically equal to eight times the instantaneous velocity. Analyze the displacements for t --> infinity.
Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.
Consider the given wing vibration model, determine the equations of motion of the system. Note that the “G” is the center of mass and “e” is the distance to the point of rotation.
A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is released from a point 10 cm below its equilibrium position with an upward velocity of 15 cm/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to twelve times the instantaneous velocity. Find the position function (the equation of motion) if the mass is driven by an external force f(t)=40cos(5t).
A body weighing 5kg is attached to a very light bar as depicted below. The set-up is free to rotate in the vertical plane about pin support O. The force applied at point C makes the bar oscillate(via small rotation) about the position of equilibrium illustrated below With the motion equation being the answer for 2a and amplitude and phase angle being the answer for 2b, Present the differential equation of motion to include the amplitude and the phase angle
A uniform plank of mass 2.29kg and length 39.6 cm is pivoted at one end, and the opposite end is attached to a spring of force constant 454N/m. The height of the pivot has been adjusted so that the plank will be in equilibrium when it is horizontally oriented as in the figure. Find the period of small oscillation about the equilibrium point. Answer in units of s.
A spring, with a 54 lb/in spring constant, is mounted on a vertical wall to support a 64.4 lb mass. At t=0 and an initial velocity of 9 in/sec. to the left, the mass is released from a position 2 inches to the right of the equilibrium position. Determine: a. Angular frequency
When suspending a load, an ideal spring was stretched Δ y = 9.8 cm If the decrease logarithmic is δ = 3.10 Show that the equation for the period of oscillation of the charge is:
My question and answer is in the image. A 6-foot spring measures 7 feet long after a mass weighing 4 pounds is attached to it. The medium through which themass moves offers a damping force numerically equivalent to 2 times the instantaneous velocity.(a) Find the equation of motion if the mass is initially released from the equilibrium position with an upwardvelocity of 4 ft/s. (Use the convention that displacements measured below the equilibrium position are positive). y = ((2-sqrt(2))/2)e4(sqrt(2)-2)x-(2-sqrt(2)/2)e-4(2+sqrt(2))x (b) What type of motion does the solution of the initial value problem describe? (free undamped (simple harmonic)motion, free overdamped motion, free critically damped motion, or free underdamped (oscillatory) motion) Free overdamped