I'm in a ditch here so-to-say in finding out the mathematical truth that underlies all projects such as these. I'm trying to build a pendulum that has a period or [ time for one swing back and forth ] of 1.6 seconds. Although I could simply calibrate it with numerous attempts of comparisons in time, I'd rather actually learn how to find the answer mathematically. Every-time I conjure up some answer, it turns out to have the effect of about ~2-10 seconds off my goal at 1.6 second per Period. Can anyone tell my where my faults are made?
Here is what I have:
My Goal ~ 1.6 Seconds per Period
G= Gravitational acceleration (And yes, I'm using the accepted average of 9.81 m/sec²)
For my Frequency, since my time is already known, I am using the reciprocal (1/1.6) of my time. F= .625 Hz
Since I know both my frequency and time, all I need is the length. That's the problem.
I did the equation L = g/(4n²f²)
So Length= 9.81 m/sec²/ (4*9.869604401*.625) = .397584325 m/sec²
Which converts over to 39.75843246 cm as equal to L
To check my answers, I used these equations for frequency and time:
I have more than triple checked myself. I've plugged in other number and estimates and tested them all out.
In the end, once I apply the length I obtain through math to my pendulum, the results are far from my predictions.
For the pendulum itself, I am using 7 pretty big washers and for the 'string' I have used both string and dental floss. I've reduced the friction at the fulcrum or top of the pendulum as much as possible. Really though none of these factors except perhaps friction should even effect the outcome! Does anyone see an error in my calculations?
Thanks for reading!
EDIT- I seem to be getting closer! Dental Floss produces the least amount of friction and I am within .01~.2 away from exact timing but this is from calibration. From Math, I am getting closer to 3 seconds off the 'ticker' so to so. A last question, for the length of the 'string' of whatever you want to substitute; Do I include the half inch string that is attached to the hole in the washers? Or do I cut the length at the knot that proceeds to the top?
Like this: O>----- The "O" is the weight, which has a hole in the middle. The ">" is the part of the string that is ties into a knot around the washers (weight), and the "-----" is the main part of the string.