# Search results

1. ### Natural Frequency of a Spring System

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: In the...
2. ### Natural Frequency of a Spring System

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.
3. ### Natural Frequency of a Spring System

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...
4. ### Integral using hyperbolic substitution

Aha! I was wondering how it got to that step. Thanks very much for your help!
5. ### Integral using hyperbolic substitution

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?
6. ### Integral using hyperbolic substitution

[tex]\begin{eqnarray*} \int\left(1+x^{2}\right)^{\frac{3}{2}}dx & = & \int\left(1+\sinh^{2}\left(u\right)\right)^{\frac{3}{2}}\cosh\left(u\right)\, du\\ & = & \int\sqrt{\left(\cosh^{2}\left(u\right)\right)^{3}}\cosh\left(u\right)\, du\\ & = &...
7. ### Integral using hyperbolic substitution

Homework Statement \int\left(1+x^{2}\right)^{\frac{3}{2}}dx Homework Equations 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...
8. ### Linear second order non-homogeneous ODE question

Aha! Of course. It's all so simple once you know what to do... :rofl: Thanks very much!
9. ### Linear second order non-homogeneous ODE question

I'm not sure I understand this. Are you able to explain it a little more? Cheers
10. ### Linear second order non-homogeneous ODE question

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...
11. ### Any ideas on what material this is?

Hi everyone, I'm having trouble identifying the material used in the oil seal of a hydraulic gear pump. There is a picture of the microstructure of the oil seal with it's hardness. Any ideas? Cheers
12. ### Electric Flux Through A Box

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...