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Hi, friends.
Is there a way to solve the symbolic solution for a vibration system in mathcad?
Such as f(t)=0, and the solution should be in the form of Asin(wt+a)+Bcos(wt+a)
Thank you in advance!
Looking forward to your help!
Shawn
Solved! Go to Solution.
Ah, you wanted the general, symbolic solution. Well here goes:
Success!
Luc
Mathcad cannot solve differential equations symbolically.
Hi, Richard,
What if I define the values for these parameters?
say:
m=10, mb=5, E=29000, I=500, L=15.
Is it possible to find the function of v(t)?
Thank you
Not using the symbolic processor, no. I don't know if it can be solved using Laplace transforms, it's not something I have any experience with. LucMeekes seems to be kind of a whiz at that though, so maybe he can give an opinion (or, even better, a solution!)
Yeah, I just visit Luc's post, it is fabulous.
Laplace transform works great!
Thank you very much!
Please post your solution here to help others.
Mike
Hi, Mike
The attachment is how I used the method of Laplace Transform to solve the equation.
Hope that could help.
Best
Shawn
Hi Shawn,
Good to know that my work is inspiring.
You give:
as the "governing equation", I interpret that as 'the solution'.
For this v(t) it follows that
Much different from the initial conditions that you state:
which are again different from the ones that you actually use:
You should get:
The mistake is where you substitute the expression for c into v(t). you're effectively using v(t) - 1 rather than v(t), so you end up with a 'governing equation' for v(t) - 1.
Success!
Luc
Thank you for your correcting.
My work still needs improving.
Your example is really inspiring and you are the best!
BTW, May I ask the reason that you collect the inverse laplace with sin(2t), cos(2t) and exp(t) in this step:
Is it because you found the term on the left side can be traced back to the basic laplace transform like laplace(sinat)= a^2/(s^2+a^2)?
Or collect the inverse laplace with sin(2t), cos(2t) and exp(t) is a universal method in this step?
Thank you for your help!
Shawn
It's certainly not universal (contrary to the formula I use to solve linear differential equations of any order with constant coefficients).
The collection is a remnant of a solution for another problem.
In general the result of the invlaplace is a complicated and 'messy' expression. I usually inspect it to see what are usefull elements to collect. After judiciously choosing the parts for collection the expression often becomes more understandable.
In your case there was a single sine, not with 2t as argument, so the collection didn't do anything.
Success!
Luc
Got ya.
I think it might be better off for me to go review some of the basics of Laplace Transform
before utilize it in Mathcad.
Thank you, man!
Ah, you wanted the general, symbolic solution. Well here goes:
Success!
Luc
You are my hero, Savvy!