Question

pendulum

Answer 1

I have a little trouble understanding the equation 1. will you help elucidate this for me?

Answer 2

I am not sure if I've used the equation 1 correctly.

Answer 3

i dont knw how to derive that.... il have to think... better tag someone else...

all i knw is
**L = length of pendulum,
**g = constant.
**period doesnt depend on mass of bob

Answer 4

who do you think would be able to explain this better? I just want to know how the infinite series is applied, and sin^2…. +9/64 sin^4 θ/2…?
I am lost with 9/64 and even lost with sin^4

Answer 5

@experimentX @Saeeddiscover may be having some idea :)

Answer 6

@aaronq @wio

Answer 7

You need the second-order approximation or first-order approx in theoretical part of your experiment?

Answer 8

I used the 2nd equation: T=2*pi*sqrt(L/g) on angles 5, 10 and 20 since those are ≤20
I just don't know if I am doing the 45° and 60° utilizing the 1st equation.

I've tried using it for the 45° but I am not even sure if I am doing it right, so I attached a copy of the excel formula input that I have.

Answer 9

second order approximation is not precise at predicting T increase as angle increases, which what my data shows.
if you noticed that the value of theoretical up until 20° that is the case, but experimentally, there's some increase.

Answer 10

second order approximation is not precise at predicting T increase as angle increases, which what my data shows.
if you noticed that the value of theoretical up until 20° that is the case, but experimentally, there's some increase. There is a small margin of error that may be negligible, but apparently as the angle increases the larger the error, which has to be fixed.

Answer 11

In general, to obtain the 2nd equation, You mustn't use angles greater than 5. But we have found using the fact that theta = tg thta for angles very close to zero. so the greater the angle you choose, the larger the error value.

Answer 12

I misspoke at my last reply, I meant it as first-order approximation.
it says to use it ≤ 20° so that's what I am doing, which I don't really have a problem with.
what I am not understanding is

Answer 13

what I am not understanding is the series portion of the first equation…

Answer 14

You don't need to consider the series terms at all. what you need to use is to apply the 2nd equation. But equation 1 gives more precise value for an arbitrary angle theta which is smaller than 5 degrees than 2nd equation.

Answer 15

alright, I am sticking to the 2nd equation. thank you

Answer 16

It is what you should do. you don't need to apply the first equation. take care!

Answer 17

at the end of this calculation, my g is 9.6m/s^2 lol

Answer 18

It looks like the series expansion for e\(^\theta\)

Answer 19

Did you apply angles greater than 20?