me445_hw2_soln

# me445_hw2_soln - x3 = v0 wnt exp-wnt figure(1 hold on...

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1 ME 445 Mechanical Vibrations // Fall 2009 Homework #2 Solutions Problems 1 and 2 % ME 445 // Fall 2009 // Safak % MATLAB Code for Problem #1 x0 = 0; v0 = 1; wnt = 0:0.01:20; % calculate x(t) for zeta = 2, overdamped zeta = 2; A = v0/(2*sqrt(zeta^2-1)); B = -A x1 = A * exp((-zeta+sqrt(zeta^2-1)) * wnt) + B * exp((-zeta-sqrt(zeta^2-1)) * wnt); % calculate x(t) for zeta = 0.5, underdamped zeta = 0.5; x2 = exp(-zeta * wnt) .* sin( sqrt(1-zeta^2)*wnt) * v0 / sqrt(1-zeta^2); % calculate x(t) for zeta = 1, critically damped

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Unformatted text preview: x3 = v0 * wnt .* exp(-wnt); figure(1) hold on plot(wnt,x1) plot(wnt, x2, '--' ) plot(wnt, x3, '-.' ) xlabel( 'w_nt' ) ylabel( 'xw_nt/v_0' ) legend( '\zeta = 2' , '\zeta = 0.5' , '\zeta = 1' ) title( 'ME445 Homework #2, Problem #1 Free Vibration Response Graphs' ) Output: 2 4 6 8 10 12 14 16 18 20-0.1 0.1 0.2 0.3 0.4 0.5 0.6 w n t xw n t/v ME445 Homework #2, Problem #1 Free Vibration Response Graphs X: 1 Y: 0.3679 X: 0.76 Y: 0.2186 X: 1.18 Y: 0.5461 ζ = 2 ζ = 0.5 ζ = 1 2 3. 3 4. 5....
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me445_hw2_soln - x3 = v0 wnt exp-wnt figure(1 hold on...

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