mi Fortce, T m2 fakce, f Ko free, A. Why do we use Lagrange\'s Equation for vibr

Question

mi Fortce, T m2 fakce, f Ko free, A. Why do we use Lagrange's Equation for vibration related problem? I1 points B. write down the general Lagrange's Equation. 11 points! C. How many degree of freedom for the above problem? [1 points D. Is it a lumped mass or distributed mass oriented problem? [I points E. If lumped mass oriented problem, then how many lumped masses are in this system]I points F. What would be the kinetic energy equation of this system? 12 pointsl G. What would be the total potential energy equation of this system? 12 points H. Using the Lagrange's equation derive the necessary ordinary differential equations? 17 points L. How many differential equations of this system? 12 points J. How many Equation of motions of this system? [2 points] K. Does the derived differential equations represent the EOM for this system? 12 points L. Put all the derived differential equations into matrix format. 3 points

Explanation / Answer

A. It's more convenient to derive the equations of motion of a multidegree of freedom system using lagrange's equation.

B. Generalized Legrange's equation for n degree of freedom system is

d/dt(dT/dq(j)) - (dT/dq(j))+(dV/dq(j))= Q(j)^n where j = 1,2...n

C. Number of degree of freedom in this system is 3

d. Yes, it's lumped mass system, since it's connected by massless spring.

e. Number of lumped mass in the system are 3

f. m1x1+m2x2+m3x3+(k1-k2)x1+(k2-k3)x3+k3x3=F1+F2+F3

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