Problem 9: In the system shown below, the two masses are equal, and the cable is inelastic. The springs are

undeflected when = x₁ = x₂ = 0. The input is the applied force fa(t). a) Write the modeling equations in X₁ and

x2 and then find the state variable model, if the output of interest is x₁; b) find the constant elongation length of

each spring in the static equilibrium position; c) Use MATLAB command ode45 to find the static deflection

length of each spring and compare the result obtained with the answer obtained in part b. Refer MATLAB

manual, example 6/page-11. For parts b and c, take M = 1, R = 0.25, g = 9.81, K₁ = 5, K₂ = 10, J = MR²/2, B = 1

(in consistent units). Initial Conditions = 0.

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X1

ele

M

R

B

fa(t)

M

ele

K₁

X2