Im supposed to calculate the distance traveled by a pendulum and I need the formula | Mathematics | Page 1

upper crescent Oct 24, 2024, 8:36 PM

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The length of the pendulum is 50cm, the displacement is 10cm and it is on earth but the gravity is rounded up to 10. I don't need the answer, I just need the formula since I need it for a python coding course

modest shoreBOT Oct 24, 2024, 8:36 PM

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upper crescent The length of the pendulum is 50cm, the displacement is 10cm and it is on earth ...

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wanton spindle Oct 24, 2024, 8:37 PM

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are you looking for the arc length of the path the end of the pendulum takes?

upper crescent Oct 24, 2024, 8:37 PM

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Im looking for the arc length after 3 seconds

wanton spindle Oct 24, 2024, 8:38 PM

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length or displacement?

upper crescent Oct 24, 2024, 8:38 PM

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the displacement is 10cm

wanton spindle Oct 24, 2024, 8:38 PM

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right, to start with

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if we're solving for final displacement the answer is going to be different than if we solve for the total distance the pendulum travels

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the final displacement is only relative to its start and end position

upper crescent Oct 24, 2024, 8:40 PM

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that makes sense yea

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the formula i found so far is A sin(2pit/T)

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but when I put it in python the number that comes out is not the exact same as what its supposed to be as annotated

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hold on ill screenshot what I have

wanton spindle Oct 24, 2024, 8:45 PM

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upper crescent the formula i found so far is A sin(2pit/T)

this is solving for angular velocity, not displacement

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actually not even that

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use cos in that function

upper crescent Oct 24, 2024, 8:46 PM

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when I do that makes it even worse

wanton spindle Oct 24, 2024, 8:47 PM

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what is the lower case t in your formula?

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angular displacement = Acos(ωt), where ω = 2pi/T

upper crescent Oct 24, 2024, 8:48 PM

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1 second is lower case t

wanton spindle Oct 24, 2024, 8:48 PM

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is 3 seconds your period, or is that the total time the pendulum is swinging for

wanton spindle Oct 24, 2024, 8:48 PM

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upper crescent 1 second is lower case t

no i mean why do you have it.

upper crescent Oct 24, 2024, 8:49 PM

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oh just cause it was in the formula I saw, I know it doesnt make a difference

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the answer that is supposed to come out is annotated as 0.06599551597515042

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the one I get with my formula is 0.06249700733728915

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and the one I get with Cos is 0.07806487093362051

wanton spindle Oct 24, 2024, 8:50 PM

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are you inputting degrees instead of radians?

upper crescent Oct 24, 2024, 8:51 PM

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i am not inputting any degrees

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it says the pendulum is initially at reat

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rest

wanton spindle Oct 24, 2024, 8:53 PM

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yes, but it is starting with a 10cm displacement (i imagine from statinc equilibrium, unless you have a wall that the pendulum is sitting relative to)

upper crescent Oct 24, 2024, 8:53 PM

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i dont

wanton spindle Oct 24, 2024, 8:54 PM

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draw this out in a fbd itll be much easier

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this is more physics than it is math

upper crescent Oct 24, 2024, 8:54 PM

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yea i just started uni

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i wish i knew what fbd means

wanton spindle Oct 24, 2024, 8:54 PM

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free body diagram

upper crescent Oct 24, 2024, 8:54 PM

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the circle diagram right

wanton spindle Oct 24, 2024, 8:54 PM

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its just a simple drawing of the system and any forces

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no not a venn diagram

upper crescent Oct 24, 2024, 8:55 PM

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no i know

wanton spindle Oct 24, 2024, 8:55 PM

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lemme make one and demonstrate what i mean

upper crescent Oct 24, 2024, 8:55 PM

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i mean the circle with the pendulum in it

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thanks

wanton spindle Oct 24, 2024, 8:59 PM

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actually you dont need to worry about forces here

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ignore the right thing

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so im assuming you need to find the displacement m travels after 3 seconds?

upper crescent Oct 24, 2024, 9:02 PM

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yea

wanton spindle Oct 24, 2024, 9:03 PM

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So your formula should look like A * cos(ωt + θ)

upper crescent Oct 24, 2024, 9:03 PM

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but how do I calculate theta

wanton spindle Oct 24, 2024, 9:03 PM

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basic trig, its arctan(50/10)

upper crescent Oct 24, 2024, 9:04 PM

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arctan length / displacement?

wanton spindle Oct 24, 2024, 9:04 PM

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no excuse me its arctan(10/50)

upper crescent Oct 24, 2024, 9:04 PM

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other way around

wanton spindle Oct 24, 2024, 9:04 PM

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upper crescent arctan length / displacement?

not quite

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so tanθ = opp/adj

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we know the lengths of both the opposite and adjacent sides which is why i picked tangent

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then use the inverse operator to solve for theta

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so roughly 0.197

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now you need to solve for omega, which is 2pi/T

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t is the period, the time it takes the pendulum to complete one swing back and forth

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you'll need to use some angular kinematics equations to find that

upper crescent Oct 24, 2024, 9:08 PM

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i already got omega and the period

wanton spindle Oct 24, 2024, 9:10 PM

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oh perfect then youre done

upper crescent Oct 24, 2024, 9:11 PM

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wellllll

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i still get the wrong answer

wanton spindle Oct 24, 2024, 9:12 PM

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are you using t = 3

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and A = 10

upper crescent Oct 24, 2024, 9:12 PM

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yes

wanton spindle Oct 24, 2024, 9:12 PM

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how did you calculate omega

upper crescent Oct 24, 2024, 9:12 PM

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the period or frequency

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for us omega_0 is meant to be frequency

wanton spindle Oct 24, 2024, 9:13 PM

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oh thats why

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omega is 2pi times the frequency

upper crescent Oct 24, 2024, 9:13 PM

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which i did with 1/(2pi square root of (L/g))

wanton spindle Oct 24, 2024, 9:14 PM

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multiply your current value of omega times 2pi

upper crescent Oct 24, 2024, 9:14 PM

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it comes out even more wrong

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lemme take a picture of my code i hope its understandable

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rn_image_picker_lib_temp_195de538-5460-4cf0-8346-373fc22a0c32.jpg

wanton spindle Oct 24, 2024, 9:15 PM

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sweet python

upper crescent Oct 24, 2024, 9:17 PM

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could it possibly be that i have the right answer and my prof is wrong

wanton spindle Oct 24, 2024, 9:17 PM

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g/L = omega^2

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aka omega = sqrt(g/L)

upper crescent Oct 24, 2024, 9:17 PM

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omega is the frequency here or period

wanton spindle Oct 24, 2024, 9:18 PM

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neither

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angular frequency

upper crescent Oct 24, 2024, 9:19 PM

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yea my brain is melting

wanton spindle Oct 24, 2024, 9:19 PM

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sorry mate

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id do some youtubing on simple harmonic motion before attempting this, should clear things up

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im still not 100% sure what your prof is asking tbh

upper crescent Oct 24, 2024, 9:20 PM

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ill do that then, i spent 6 hours today already on this one problem despair

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thanks for your help man

upper crescent Oct 24, 2024, 9:20 PM

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wanton spindle im still not 100% sure what your prof is asking tbh

yea honestly prof just might be wrong

gloomy shoreBOT Nov 7, 2024, 6:05 PM

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@upper crescent

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upper crescent Nov 7, 2024, 6:14 PM

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oh my fault B

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+close

gloomy shoreBOT Nov 7, 2024, 6:14 PM

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upper crescent +close

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#Im supposed to calculate the distance traveled by a pendulum and I need the formula