>A broken clock is right two times every day
What if my clock (B) was broken in such a way that it ran at 1.5x the speed of a reference clock (A)? How many times on average would it he correct every day?
What if my clock (B) ran in reverse at half the speed of clock (A)?
What if clock (B) accelerated over time at a rate of X^2?
Can you generalize this into a formula to determine the maximum, minimum, and average number of times clock (B) would be correct with respect to clock (A) on any given day?
Broken clock usually means clock that doesn't run at all though
The rest of your question is just high school level physics problem, and probably your homework
>>7755688
Is that your way of saying you can't solve the problems?
The difference of amounts of revolutions per day is equal to the number of intersection as long as they have constant speed.
>>7755623
just simulate it with mcmc in matlab
>>7755693
It's my way of saying I won't solve your homework problems
>>7755702
Op here, I haven't had homework for over 4 years. This was just a thought experiment that popped into my head after someone used that saying in conversation with me earlier today.
I've only got as far as finding solutions for the set of equations, e.g. For half speed
A=2B
A%12=B%12
0<=A<=24
0<=B
There are two solutions, A=0,24 B=0,12
So the clock is right twice a day. It gets more difficult when you try to make a meta formula that can count the number of solutions. It's even more challenging when you introduce acceleration on clock B as you can't restrict A/B to 24 hours because they get out of phase
>>7755714
its not really that hard , just integrate your time formula minus your constant speed rotation formula to find the number of rotations
>>7755736
\operatorname{mod}\left(x,12\right)\ \left\{0\le x\right\}
\operatorname{mod}\left(f\left(x\right),12\right)\ \left\{0\le x\right\}
\operatorname{abs}\left(\operatorname{floor}\left(\frac{x-f\left(x\right)}{12}\right)\right)\left\{0<x\right\}
case 1
f\left(x\right)=1.5x
case 2
f\left(x\right)=-0.5x
case 3
f\left(x\right)=x^2
>>7755827
oops, I dont know how to format equations, just paste the lines into https://www.desmos.com/calculator
>>7755829
that sure worked like a charm
>>7755840
You need to paste each line one by one
>>7755840
Or I can just save it
https://www.desmos.com/calculator/iwzya4jk4y
>>7755841
ok better, ty
>>7755850
I dont understand... It works perfectly in my browser...
Try the link
https://www.desmos.com/calculator/iwzya4jk4y
>>7755850
Oh I do understand, you cant have f(x)=1.5x and f(x)=-0.5x at the same time, delete on of them
>>7755827
yeah something like that
you probably want to convert into circular coordinates and just use e^i \theta
if you allow the function to go backwards and forwards you probably need to use an absolute value metric and some kind of indicator function for counting
>>7755623
yes
>>7756093
/thread
>>7755623
That's not what a broken clock means you dipshit
>>7759485
dictionary.com
[broh-kuh n]
verb
4. not functioning properly; out of working order.
>functioning, but not properly
