MAT275 Matlab5 .docx - MAT275 Matlab5 Buyun Ma Exercise 1(a...

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MAT275 Matlab5 Buyun Ma Exercise 1 (a) By taking the derivative of the function: y = y (t), you get "v", which is the blue curve. (b) The period of Omega naught is 1.5. (c) According to the chart given, the mass will not stand still due to the presence of gravity and the absence of friction in the system that limits mass. (d) The amplitude for y oscillations are between -1.25 and 1.25, respectively. (e) (t,v) (4.8170,1.1473) (409451,1.2143) (5.0845,1.2366) (5.2240,1.2050) (5.3634,1.1206) The maximum velocity is 1.2366 when t is 5,0845. (f) If "k" (stiffness) increases and the mass is smaller, the speed will decrease proportionally. If "m" (mass) is increased, the vibration is smaller. If the mass decreases, negate it.
Exercise 2 LAB05ex2.m c lear all; % clear all variables m = 4; % mass [kg] k = 9; % spring constant [N/m] c = 4; % friction coefficient [Ns/m] omega0 = sqrt(k/m); p = c/(2*m); y0 =-0.8; v0 = 0.3; % initial conditions [t,Y] = ode45(@f,[0,15],[y0,v0],[],omega0, p); % solve for 0<t<15 y = Y(:,1); v = Y(:,2); % retrieve y, v from Y E = (1/2)*m*v.^2+(1/2)*k.*y.^2;
figure(1); plot(t,y,'bo-',t,v,'r+-');% time series for y and v grid on; axis tight; figure; plot(v,y); grid on; %---------------------------------------------------

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