You're right. As \phi goes to 90 degrees, the natural frequency should decrease to 0, as there would be no component of force acting in the x-direction then. It appears as though multiplying by cosine would make this correct, but I don't know where that comes in in the working:
I worked through it again and found the natural frequency to be:
sqrt(4k/m)/(2 * Pi).
I basically let the angles on both sides change by phi +/- dphi, and the same with the length L -/+ dL, and with x. If this is the correct answer then I suppose it worked out ok.
A mass m is confined to move in a channel in the x-direction and is connected to four identical springs with spring constant k, which are oriented at angles \phi = 45° as shown, if the system is in static equilibrium.
a) Ignoring friction, determine the natural frequency of vibration of the...
Oops, that was meant to be nice neat LaTeX...
Well, I tried doing that but ended up with int(cosh^4(u))du... not sure if there is a nice little trick for solving that or if I've ended up with a harder problem than I started with. Also, why didn't that tex code just work?
The hyperbolic functions.
The Attempt at a Solution
We've been going over hyperbolic substitutions in class so I assume I'm meant to use one of those, but I'm just not sure how to choose which one. Any help...
Determine the general solution to the ODE:
y'' + 2y' = 1 + xe-2x
I know the solution will be of the form y = yh + yp. The homogeneous solution is y = c1 + c2e-2x.
For the particular solution, I have been using the method of undetermined coefficients. c3e-2x won't work as it is not...
So you've been given the angle theta which is 13 degrees.
You'll need to find the cross sectional area which will be given by the distance x multiplied by the height of the box which I believe is given by the question.
The angle that you need to work out the length of x is also in the...
Should there not also be a force due to friction pointing back up the slope? When you put that into your free body diagram have a look at all the individual x and y components of each force, F_n, f_s and F_g.
I'm trying to solve an ODE using MATLAB and Euler's method but I've having some trouble understanding what's going on with the code. This is something relatively simple but I'm new to MATLAB so I'm not really sure what's going on.
Write a Matlab M-file that uses Euler’s method to...
In this case isn't m the fringe number and not the fringe number per unit length? I stumbled upon another answer that said m/x was 2*theta/Lambda which gives you a value. I'm not sure about that though because surely you need to know the distance the "viewing screen" (in this case the glass) is...