Can anyone answer this problems using Laplace Transform and Partial Fraction Expansion?

1.) d^2x/dt^2 + 6dx/dt + 8x = 5sin3t
2.) d^2x/dt^2 + 8dx/dt + 25x = 10 u(t)
3.) d^2x/dt^2 + 2dx/dt + x = 5e^-2t

Thanks.

Well, have you made an attempt at the answer? We can't just do your homework for you.

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Originally Posted by Capuchin

Well, have you made an attempt at the answer? We can't just do your homework for you.

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Yes of course, I have used 3 papers trying to answer them.

Here are my answers:

1.) my answer is probably wrong

2.) -10/25 e^-4t cos3t -4/15 e^-4t sin3t - 10/25

3.) 5 e^-2t + 5te^-t - 5e^-t (Probably Correct)

Do you have initial conditions you forgot to post? LaPlace usually comes with initial conditions. Just checking. y(0)=? y'(0)=? for example.

Oh yes, I'm sorry, I forgot, the initial conditions are y(0)=0, y'(0)=0

But I think that the initial conditions is used on the "Direct Method", while Laplace Transform don't need initial condition.. I'm not sure actually, any opinion would be greatly appreciated.

I will help with the first one. You see if you can finish, OK?



Use Laplace subs:



Factor out and solve for Y:





Partial fractions:



Now, use the inverse Laplace that correspond with the respective elements of the partial fraction decomposition. . I assume you have the table. That's what I use.

Write back if you're still stuck.