C. Lagrange's Equations - The Third Method for Analysis 1) Force Analysis (Newtonian) 2)...

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C. Lagrange's Equations - The Third Method for Analysis 1) Force Analysis (Newtonian) 2) Displacement Analysis (Flexibility) 3) ENERGY METHOD (Lagrange's) - For low-damped systems • For systems where elastic member has significant mass (Beams)
CONSERVATION OF ENERGY Kinetic Energy = T =1/2mie Potential Energy = V = 1/21a2
Then T + V = Constant
and —d (T +V) = 0 dt
d ( mi2 kx21 = (m kjoi = 0 d4 2 2
La- mf + kx = 0 caa

David · Accepted Answer

Given the problem as shown below in diagram. Here, we get that the change in Potential energy and Kinetic
Energies for the given 2-Degree of Freedom(DOF) system between initial and final position is obtained as follows.Note
that x(t) is the diaplacement of the mass M & θ(t) is the angular displacement of the pendulum from vertical. So,

C. Lagrange's Equations - The Third Method for Analysis 1) Force Analysis (Newtonian) 2) Displacement Analysis (Flexibility) 3) ENERGY METHOD (Lagrange's) - For low-damped systems • For systems where...

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