While watching my daughter twirl around on a merry-go-round (okay you got me, this picture is not my daughter), I was thinking about the implications of periodic functions. Obviously, if this merry-go-round continued spinning indefinitely at a constant speed, a basic periodic function would do the trick. But what about a more real world situation?
The merry-go-round slows down to a stop, stops for a short time, speeds back up and then does its spinning again. How would you write a function for that? And to make it even more complicated, sometimes the merry-go-round stops for longer or shorter intervals to allow for more or less kids to get on. I know a periodic function must repeat, but could you use an extra variable in there to represent the different lengths of times that it stops? Use some numbers if you like, but I would be very interested in your responses even with just variables to represent the different parts of this problem. Thanks in advance!
~ Curious math teacher here; read my introduction post! :)
https://steemit.com/introduceyourself/@melek/punish-a-white-kid-first-the-rule-i-didn-t-follow
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I'll give you my upvote.
Please reciprocate in my post - https://steemit.com/introduceyourself/@gustavopasquini/2h1hhg-hello-steemers-new-member-introduced-in-steemit-community-video
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Of course you can!
Consider something like the following:
A_1(t)sin(w_1(t) t) + A_2(t)cos(w_2(t) t)
You allow A_1, A_2, w_1, and w_2 be functions of time, that will change amplitude and frequency.
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Thanks! I'm playing around with it now. I'm grateful for people so much smarter than me taking the time to respond to my questions. I've read your posts and they are awesome. :)
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This reminds me of some classical mechanics problems I encountered in college. Add a spring (like with Hooke's law) on a merry-go-round that is 10 meters from the center. Find the net force on the object after 5 seconds. Oh yeah, the merry-go-round has been pushed off a cliff and don't ignore wind resistance. All kidding aside, I always would start with a free-body diagram to try to my head around the problem. There must be some acceleration in the problem being that it is not going at a constant speed. At t=0, the velocity is zero. At t= whatever, it is at max velocity.
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You just need to use
:p sorry, it's early here... upvoted
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