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A lkg mass is suspended from a spring with spring constant k = 1 and damping cocfficient y 0.125. An external force is applied F = should take the Laplace transform, solve for Y, then use Wolfram Alpha to get plot the inverse Laplace transform (i.c. solution to the differential cquation) for 0

A lkg mass is suspended from a spring with spring constant k = 1 and damping cocfficient y 0.125. An external force is applied F = should take the Laplace transform, solve for Y, then use Wolfram Alpha to get plot the inverse Laplace transform (i.c. solution to the differential cquation) for 0

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6. Use Wolfram Alpha on the following problem: A 1kg mass is suspcnded from a spring with spring constant k = 1 and damping coefficient y= 0.125. An external force is applicd F = 3 cos(3t). The initial conditions are y(0) = 2 and y'(0) = 0. You should take the Laplace transform, solve for Y, then use Wolfram Alpha to get plot the inverse Laplace transform (i.c. solution to the differential cquation) for 0 <t< 60. Hcre is an example: plot inverse Laplace transform (s^3-25^2-6s-6)/(s^4+4s^3+24s^2+4s+10) for t from 0 to 20 t from 0 to 20. 10 15 -0.5 If you just ask for the inverse Laplace transform it will give it to you. The parent program, Math- ematica, computes the inverse Laplace transform using a contour (path) integral in the complex plane. Ask me about these outside of class if you like. In any case, the output involves i's. You can find the real form in the list of alternate forms below the graph. The answer for this problem is frightening!
Transcribed Image Text:6. Use Wolfram Alpha on the following problem: A 1kg mass is suspcnded from a spring with spring constant k = 1 and damping coefficient y= 0.125. An external force is applicd F = 3 cos(3t). The initial conditions are y(0) = 2 and y'(0) = 0. You should take the Laplace transform, solve for Y, then use Wolfram Alpha to get plot the inverse Laplace transform (i.c. solution to the differential cquation) for 0 <t< 60. Hcre is an example: plot inverse Laplace transform (s^3-25^2-6s-6)/(s^4+4s^3+24s^2+4s+10) for t from 0 to 20 t from 0 to 20. 10 15 -0.5 If you just ask for the inverse Laplace transform it will give it to you. The parent program, Math- ematica, computes the inverse Laplace transform using a contour (path) integral in the complex plane. Ask me about these outside of class if you like. In any case, the output involves i's. You can find the real form in the list of alternate forms below the graph. The answer for this problem is frightening!
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