New answers tagged degrees-of-freedom
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Conjecturing the homogeneous solution of a $2^{nd}$-order constant coefficients ODE - why conjecturing a $3$ D.O.F. solution in this course?
Although it looks like there are 2 complex constants A and Z, which is 4 real degrees of freedom, the ODE will actually fix Z completely, and so you really only have the 2 real degrees of freedom for ...
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Conjecturing the homogeneous solution of a $2^{nd}$-order constant coefficients ODE - why conjecturing a $3$ D.O.F. solution in this course?
The original problem is to find a real-valued solution, with two real-valued integration constants. The trick he is using is to generalize the problem to finding a complex-valued solution, with two ...
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Driven $RLC$ circuit why is the permanent signal sinusoidal and why two degrees of freedom (amplitude and phase)?
that the particular solution (i.e. the permanent signal) is also sinusoidal, with the same periodicity as the RHS term function?
Answer 1: Because the system is linear.
Answer 2: Can you find another ...
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Radiative and Longitudinal degrees of freedom of EM field
Okay, reading the answer of @my2cts I've come up with a reasoning that allows me to sleep at night. The 2nd and 3rd equation are indeed the same equation, say
$$\nabla^2 \phi + \frac{1}{c} \vec{\nabla}...
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Radiative and Longitudinal degrees of freedom of EM field
The time derivative of the second equation is identical to the divergence of the third one.
Edit. So the two field components are dependent and are one degree of freedom.
In fact the charge-current ...
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