Find equation of motion and natural frequency for the system shown in fig. by energy method. H.W2// For the system Fig below find 1-F.B.D 2-Eq.of motion 8wn 4-0 (5) m. Jo m

3. Suppose the model of a vehicle suspension is given below. Write the equation of motion in matrix form (not in State Space form). Calculate the natural frequencies for k₁ k2 10 N/m, m2 = 50kg, and m₁ = 2000kg. -= - - 103 N/m, 1 x1(c) m1 www m1 Car mass k₁ Car spring k1 k₂ Tire stiffness www x2(1) m2 Tire mass м2 k₂ ↑

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Whats the first equation (circled) and how did we get it ?

Ex. A vehicle wheel, tire and suspension assembly can be modeled crudely as a single degree of freedom spring mass system. The mass of the assembly is measured to be about 300kg. its frequency of oscillation is observed to be π rad/sec. What is the approximate stiffness of the tire, wheel and suspension assembly? ilippines) Accessibility: Investigate

Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s

Derive a model for the mechanical system represented below. The input being the force F and the output the displacement x. Determine the time response, x(t) when F is an impulse force of 100 Newton. K-50 kg/s² M=10 kg B-60 kg/s F (Vol Ans: x(t) = 2.5(e¹ - es)

1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.

ll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112

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