b. Find the equation of motion of the system below using Lagrange's equation. Masses m₁,m2, and m3 are added to the compound pendulums with rod masses Mr₁, Mr2, andMr31respectively. Assume the mass of all pendulums are evenly distributed so that their centerof gravity is in the middle of the pendulum of length L. Use the small angle assumption.O○L02M1Lm3m2

All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Answered: b. Find the equation of motion of the…

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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I need answer within 5 minutes please please with my best wishes
The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x, '(0) = x2'(0) = 0) in its equilibrium position (x, (0) = x2(0) = 0) with the given external forces F, (t) = 0 and F, (t) = 270 cos 4t acting on the masses m, and m,, respectively. Find the resulting motion of the system and describe it as a %3D superposition of oscillations at three different frequencies. k2 mi ww m2 k3 - (k, + k2) k2 K= k2 - (k2 + k3) m, = 1, m, = 2; k, = 1, k, = 6, k3 = 2 %3D Find the resulting motion of the system. X4 (t) = X2(t) (Type exact answers, using radicals as needed.)
Consider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground. What is the kinetic energy of the system? Select all that apply. I don't know how to get these answers.
A car is modeled as shown in Figure. Derive the equations of motion and find matrix M, C, and K. Mass = M, mass moment of inertia = JG .000 m1 k₂ F1 1 k2 000 k₁ k₁ m2 F2, X2 ell
I need a clear and fast answer within 20 minutes. Thank you
Derive the equations of motion using Lagrange's equations. (I, =mr? ) THE MOTION IS ON THE HORIZONTAL PLANE (NO GRAVITY) Trailer, mass M Cylinder, k1 mass m k2
A uniform rod of mass M = 2.3 kg and length L = 0.2 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by 1/3 ML2. If a force F = 7 N, q = 47° acts as shown, what is the resulting angular acceleration (in rad/s2) about the pivot point?
Dynamics
Needs Complete typed solution with 100 % accuracy.
A weight with mass mw=150 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R=4.00 cm and mass Ms=200 g. Find the magnitude ?a of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. Use ?=9.81 m/s2. Find the tension T in the thread.
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…
4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.

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