Different modes of oscillation for a pendulum
The period of a simple pendulum is not a trivial thing, and it depends on the initial conditions.
Shown here are ten different modes of oscillation for the same pendulum. The only difference is the total amount of mechanical energy in the system.
As a result, each one has a completely different period of oscillation, unlike what the small-angle approximation (as taught in high-school) would suggest. They can’t be in sync. You may see some really interesting patterns based on the delay between them in your browser.
The red graph above each pendulum represents the phase portrait for the respective mode of oscillation, with the current state marked as a blue dot. The horizontal axis represents angle (hence why it wraps around the sides) while the vertical axis represents angular velocity.
Pendulums are very interesting dynamical systems, as they are relatively simple to understand but can produce surprisingly complex results in certain cases, such as the chaotic behavior of double pendulums and the odd behavior displayed by coupled pendulums.
I don’t know why I was so amused by this.
I feel like I didn’t help anything…. :(
Um… I wasn’t really asking for help… I dunno. It was just a question. It’s okay.
….okay. Honestly? All my hatred for Santana aside….. I know that you’re probably one of the only 2 people on earth that she actually cares about….. and I want to believe that she would never hurt you on purpose…. but, that being said….. Santana can’t distinguish between right and wrong. It’s not that she just doesn’t want to, it’s that she physically can’t, so…. I really don’t know. I hope not.
Do you think San would cheat on me? I mean… I know that… I dunno.
Britt…… you can talk to me about anything…. you know that, right? I love you! We’re sisters.
You don’t think Santana… You don’t… Nevermind.