L this is an individual report). SuIts and all lat Is shown beginning on page 4-

Question

L this is an individual report). SuIts and all lat Is shown beginning on page 4- a mass, m, a spring with stiffness k, and a dashpot with damping simplified model of the suspension of a car consists of coefficient c, as shown in the figure. A bumpy road can be mod- eled by a sinusoidal up-and-down motion of the wheel y = },sin(cor). From the solution of the equation of motion for this model, the steady-state up-and-down motion of the car (mass) is given by x = Xsin(or-4). The ratio between ampli- tude X and amplitude Yis given by: k-mo)+(oc) Assuming that m = 2000 kg, k = 500 kN/m, and c 38 X 103 Ns/m, determine and plot the variation in frequency, , for values of 0.1 X/Y 1 in increments of 0.05 using an MATLAB M-file written by the team for the purpose. Thoroughly discuss the effect ofXY on the frequency . Does your conclusion change ifc is doubled or halved? torhnical reports following the format ted in these reports iu teams of two or three (you will receive a grade of 0 if you work om members. You are to collaborate on the solution of

Explanation / Answer

function X = SMD(B, t, m) % ‘SMD’ for ‘Spring-Mass-Damper’ % B = parameter and initial conditions column vector (unless you want to % supply the initial conditions in this function rather than passing % them as parameters). X0 = B(3:4); % This gives you the option of passing the last two entries of the % parameter vector as the initial values of your ODE. In this case, the % curve-fitting function will also fit the initial conditions as well as % Kd and Ks. If you don't want the initial conditions to be parameters, % B becomes [2 x 1] and you define X0 as whatever you like in the % function. [T,X] = ode45(@DifEq, t, X0); function xdot = DifEq(t, x) % B(1) is the coefficient of viscous friction (‘damper’), Kd; % B(2) is the spring constant, Ks; xdot = zeros(2,1); xdot(1) = x(2); xdot(2) = -x(1)*B(2)/m -x(2)*B(1)/m; end X = xdot(:,2); % Assumes ‘xdot’ is a [N x 2] matrix where N = length(t) end

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