ANSWER PART D - USE MATLAB EQUATIONS OF MOTION BELOW FOR REFERENCE Problem 1 (yo

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ANSWER PART D - USE MATLAB

EQUATIONS OF MOTION BELOW FOR REFERENCE

Problem 1 (you may use matlab for numerical calculations: 50 points: Consider only the horizontal motion of the 4-mass system given below. Let m 2 kg and k =2 a. b. c. Develop its equations of motion using Lagrangean method. Determine the modal vectors. Transform the equations to modal (principal) coordinates and write the resulting four decoupled equations of motion Using matlab, plot the velocity response of the right-most mass d. In

Explanation / Answer

if true function fout = deriv(f, g) % deriv differentiates f with respect to g=g(t) % the variable g=g(t) is a function of time b = sym('b'); f1 = subs(f, g, b); f2 = diff(f1, b); fout = subs(f2, b, g); x=sym('x(t)'); tettapl=sym('tettapl(t)'); tettal1=sym('tettal1(t)'); tettal2=sym('tettal2(t)'); %% %Here is the calculation of the Kinetic and Potential energies %% eqn1=diff(deriv(K,diff(x)))-deriv(K,x)+deriv(P,x) eqn2=diff(deriv(K,diff(tettapl)))-deriv(K,tettapl)+deriv(P,tettapl) eqn3=diff(deriv(K,diff(tettal1)))-deriv(K,tettal1)+deriv(P,tettal1)-diff(tettal1) eqn4=diff(deriv(K,diff(tettal2)))-deriv(K,tettal2)+deriv(P,tettal2)-diff(tettal2) end

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