ylabel Amplitude u title Amplitude vs Time As e approaches positive infinity

Ylabel amplitude u title amplitude vs time as e

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ylabel( 'Amplitude u' ); title( 'Amplitude vs Time' ); As e approaches positive infinity, the amplitude and the value of u + approaches zero. e = 0.0, Amplitude = 0.9994, u + = 3.137 e = 0.2, Amplitude = 0.9586, u + = 2.905

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e = 0.4, Amplitude = 0.9277, u + = 2.770 e = 0.6, Amplitude = 0.9015, u + = 2.675 e = 0.8, Amplitude = 0.8787, u + = 2.589 e = 1.0, Amplitude = 0.8601, u + = 2.519 Question 2: Changing the value of e in (-) direction for generic nonlinear spring-mass system Note: The same code utilized in question one was also used in question two. As e approaches negative infinity, the amplitude and the value of u + approaches infinity. e = -0.1, Amplitude = 1.025, u + = 3.235 e = -0.2, Amplitude = 1.059, u + = 3.492
e = -0.3, Amplitude = 1.106, u + = 3.7755 e = -0.4, Amplitude = 1.176, u + = 4.185 Question 3: Nonlinear spring-mass system with changing w %Calculates the ODE for a specific oscillating nonlinear spring mass system function dudt = force1(t,u) dudt = zeros(2,1); dudt(1) = u(2); dudt(2) = cos(w * t) - 0.2 * u(2) - u(1) - 0.2 * u(1).^3; return end Note: “w” was replaced with specified value of omega to graph the given data. % Code used to graph oscillating second order differential equations [t,y] = ode45( 'force1' ,[0 60],[0 0]); plot(t,y(:,1), 'k' ) xlabel( 'Time t (sec)' ); ylabel( 'Amplitude u' ); title( 'Amplitude vs Time' ) After careful analysis of the graphs depicting various w ’s between 0.5 and 2.0 and the time frame 40 s to 60 s, it is visibly clear that w = 1.4 gives the largest amplitude.

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w = 0.5, Amplitude = 1.292 w = 0.7, Amplitude = 1.522 w = 1.0, Amplitude = 2.171 w = 1.3, Amplitude = 2.897 w = 2.0, Amplitude = 0.3863 w = 1.4, Amplitude = 3.055
• Spring '09
• 0.3863 w, 1.292 w, 1.522 w, 2.171 w, 2.897 w

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