Recent content by JoePhysics

That problem is a lot more complicated. Basically, instead of the one degree of freedom that you had for the simple pendulum (the angle), you have two (the angle, and the extension of the spring). The standard way to solve such a problem is to obtain the equations (note that I said it in plural)...

Yes, that is correct. The harmonically oscillating solution and associated initial angle-independent period (##T = 2 \pi \sqrt{\ell/g})## are always approximations. The point is, the small-angle approximation solution deviates very little from the actual solution when the initial angle is small...

For an arbitrary initial angle, it can be shown that the solution to such a differential equation is given by $$\theta(t) = 2 \sin^{-1}\bigg\{k ~\text{sn} \bigg[\sqrt{\frac{g}{L}}(t-t_0);k\bigg]\bigg\}$$ where ##k = \sin(\theta_0/2)## and ##t_0## is the time when the pendulum is vertical...

:welcome:

To answer your question (regardless of the video), the behavior you are looking for is known as shear-thickening: when a force/pressure is applied to the substance, its viscosity can dramatically increase, thus exhibiting behaviors characteristic of a solid and not a liquid. Stop applying the...

If I recall correctly, the way it works is that if you try impose an order in the complex numbers, you then lose the field properties.

:welcome:

I've done some searching, and this seems to be a nontrivial problem. This and https://www.researchgate.net/figure/260232817_fig3_Figure-3-Temperature-distribution-in-a-current-carrying-wire-with-finite-length-L-with seem to suggest that the differential equation that governs such a situation...

The bar has no radial dimensions, and the two masses are to be taken as point masses, so in the equation ##I_\text{CoM,parallel} = \int r^2 dm##, the ##r## is vanishing, as I understand the situation.

I am a bit confused by the statement. If this is a uniform bar, and the masses glued to its ends are to be considered as point masses, ##I_\text{cm}## through an axis that is parallel to the bar and goes through the two masses should be ##0##, right? If that is the case, the parallel-axis (aka...

That's pretty nuts. Where was this, if you don't mind? May be useful to see some examples of crazier qual exams.

It really doesn't go by hours. Go through your undergraduate books, do as many problems as you can, find previous exams from your department and do them, make sure you live, breathe and eat the basics.

Remember how these things were done with complex numbers. If you have ##z_1 = a e^{i \theta_1}## and ##z_2 = a e^{i \theta_2}##, how would you do ##z_1 z_2##?

Good analogy.

Other than multivariable calculus and linear algebra, I would certainly add differential equations, both ordinary as well as partial, as required to go through a typical undergraduate physics program.