Homework Statement
I am given a Lagrangian, which, per assignment text, describes a single degree of freedom:
L= \frac{I}{2}(\dot{q}+\omega)^2-kq^2
I need to find the Hamiltonian.
Now, what I am wondering, when performing the Legrende transform...
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The picture says a thousand words:
http://www.hot.ee/jaaniussikesed/v6rrand.jpg
In the last member under the square root, there is the error. For some reason I am not able to differentiate with an array index, ts1 is a single column 5 row matrix. How to solve this? The error says...
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I have this thermodynamical expression:
dS=\sigma T^3 dV+4V\sigma T^2 dT+\frac{1}{3}\sigma T^3 dV=d(\frac{4}{3}\sigma T^3 V)
Basically saying:
\frac{4}{3}\sigma T^3 V=S
Now, I do not get this.. d(expr) part, why are there three members to d(expr), with 2x dV and 1x dT.. nope...
Homework Statement
I have hydrogen in a 12 L tank, at T=15 C. Some of it is used, the T = const. and Δp=0.4 MPa,
the molar mass of hydrogen is M=2*10^-3 J/(mol*K). Find the mass of the used hydrogen.
Homework Equations
Am I wrong in simply using:
\Delta m=\frac{M}{RT}V\Delta p ...
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On Pauls notes webpage, there is the following problem to be solved by variation of parameters:
ty''-(t+1)y'+y=t^2 (1)
On the page, the fundamental set of solutions if formed on the basis of the complementary solution. The set is:
y_{1}(t)=e^t and y_{2}(t)=t+1
Now, I must be...
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I have some examples of non-homogeneous ODEs to be solved by the undetermined coefficients method. Two from "Pauls math notes" page:
y''+8y'+16y=e^{-4t}+(t^2+5)e^{-4t}
The compsol. for this is:
Y_{c}=C_{1}e^{-4t}+C_{2}te^{-4t}
The first guess for a particular solution would be...