Ok, so while I understand 2nd Order ODEs... I really don't understand MATLAB.(adsbygoogle = window.adsbygoogle || []).push({});

I have 2 questions that I just can't get any code to work for:

1

Question: Consider the model of an undampened spring-mass system with a time-dependent spring constant k(t) given by:

d2y/dt2 + k(t)y = 0,

Use the ODE45-solver to obtain the solution curves satisfying the initial conditions on interval [0, 100] and function k(t). Predict the behavios as t approaches infinity and discuss the nature of the oscillations (if any)

1) y(0) = 1, y'(0) = 1, k(t) = cos(t)

2) y(0) = 1, y'(0) = 1, k(t) = 1+t^2

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2

Question: Consider the following model for a linear mass-spring system with damping and forcing:

d2y/dt2 + (1/5)(dy/dt) + (1/5)y = coswt, y(0) = 0, y'(0) = 0

1) Use ODE45-solver to obtain the solution curves for values of w = 0.5, 1, 1.5, 2. Plot the solutions and estimate the amplitudeAof the steady response in each case.

2) Using the data from part 1), plot the graph ofAversus w. For what w is the amplitude greatest?

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I know how to use ODE45 to solve a 1st Order ODE and I know how to use other parts of MATLAB (tspan, y0, plot, etc.) but I have no idea how to approach this problem (mainly due to the 2nd Order ODE) nor has my professor been the best teacher when it comes to MATLAB.

Thanks!

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# 2nd Order ODE in MATLAB help

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