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Student Support Forum: 'Critically Damped Differential Equation' topicStudent Support Forum > General > Archives > "Critically Damped Differential Equation"

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Author Comment/Response
Peter Pein
09/24/06 11:14pm

Hi,

1. Solve the differential equation:
In[1]:=
sol = y[t] /. First[DSolve[m*Derivative[2][y][t] + b*Derivative[1][y][t] + k*y[t] + m*g ==
0, y[t], t]]
Out[1]=
-((g*m)/k) + E^(((-b - Sqrt[b^2 - 4*k*m])*t)/(2*m))*C[1] +
E^(((-b + Sqrt[b^2 - 4*k*m])*t)/(2*m))*C[2]

2. select the term in the sqrt:

In[2]:=
Cases[sol, Exp[y_] :> Cases[y, (s_)^(1/2) :> s, Infinity][[1]], Infinity, 1][[1]]
Out[2]=
b^2 - 4*k*m

And now you can do whatever you want with this term.

hth,
Peter


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Subject (listing for 'Critically Damped Differential Equation')
Author Date Posted
Critically Damped Differential Equation Paddy 09/21/06 5:27pm
Re: Critically Damped Differential Equation Peter Pein 09/24/06 11:14pm
Re: Critically Damped Differential Equation yehuda ben-s... 09/25/06 07:28am
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