Consider two rigid and infinitely long parallel plates (say they are of infinite length in X direction, so running from -inf to +inf in X axis) separated by a distance d (say measured in Y-direction). Let the space between the plates be filled up with a fluid that supports acoustic waves. If we...
I am trying to understand the physics of resonance phenomenon. One can find the resonant modes of a water filled spherical cavity either analytically or by using the FEM eigenvalue analysis (K-ω2n M = 0, with K and M being the usual stiffness ans mass matrices in FEM). For the later, we usually...
Is it possible to obtain a solution of the linear system Ax = b with LU decomposition when A contains zeros on its diagonal? I am trying to obtain a solution with LU decomposition and then perform a forward/backward substitution but I get NaN entries in the solution vector x. The condition...
Consider a circular pin-in-a-hole problem in two dimensions. Let the plate containing the hole be infinite so that the dimensions of the circular pin are very small compared to the plate. The conditions of plane stress be assumed everywhere. Also, let the pin be loaded with a force applied at...
@vanhees71: I should have probably said that s is the unit tangent at point P. Physically, what I need is the second derivative of x coordinate at point P with respect to the unit tangent s at P (i.e. d2x/ds2). This can also be interpreted as the rate of change of x-component of unit tangent s...
Let P(x,y) be a point on a unit circle that is centered at (0,0). How to compute exactly the function
\frac{\partial^2 x}{\partial s^2}
where x is the x-coordinate of the point P(x,y) and s is the tangent at point P(x,y) . Clearly,
\frac{\partial x}{\partial s} =...
Consider a plane sound wave (\varphi^i) incident up on a solid object . The object will scatter this incident wave. Let this scattered wave pass through an interface separating two different fluids (say with sound speeds c1 and c2). Now at the interface, is the scattered velocity potential...
There was an error in dr/dθ:redface:
\begin{equation}
\frac{dr}{d\theta} = -5*\sin(10\theta)
\end{equation}
I tried http://www.wolframalpha.com/input/?i=integrate+sqrt%28%281%2B.5*cos%28N*theta%29%29^2%2B%28-N%2F2*sin%28N*theta%29%29^2%29+d%28theta%29 but the page times out. Do I need a...
I missed dθ in Eq. (2) in my post above. The second equation should read
\begin{equation}
s = \int\limits_{\theta = 0}^{\theta = 1.0} \sqrt{r^2 +\left(\frac{dr}{d\theta}\right)^2} d\theta
\end{equation}
I have a curve defined by following parametric equation:
\begin{equation}
\gamma(\theta) = 1 + 0.5 \times \cos (N \theta) (\cos(\theta),\sin(\theta)), 0 \leq \theta \leq 2 \pi \
\end{equation}
I need to calculate the length of the curve between say θ = 0 to θ = 1.0...