Find Universal Gravitational Constant w/ Torsion Balance Timelapse Recording

[guyvsdcsniper]

Homework Statement

Find the universal gravitational constant

Relevant Equations

F=Gm1m2/r

I am using pasco's gravitational torsion balance https://www.pasco.com/products/lab-apparatus/fundamental-constants/ap-8215 to find the universal gravitational constant in a lab report.

Two large tungsten masses are positioned close to two smaller masses, causing the torsion balance to oscillate. The balance has a mirror attached to it. A laser is shined on the mirror and reflected on a background. The laser will move with the oscillation of the balance as it oscillates to its equilibrium position. It moves as a damped harmonic oscillator.

I recorded the oscillation of the laser using a timelapse video on my 4th gen iPad pro. Googling, I found the timelapse has a frame rate capture of 1 frame every 4 seconds for videos over 40 minutes (i recorded for 45 minutes). This speed relative to time is 120x.

The problem is that while the data taken from these videos is very useful for tracking the equilibrium position of the laser, the time is a lot more compressed. So my data shows the total oscillation recording in about 25 seconds.

The only thing I can use from this data is find the centerline of the oscillation so I can get an approximate equilibrium point position since the time is so off. The time being off is bad because I need to calculate the period of the oscillations as G is inversely proportional to $T^2$.

My solution is just use a video I recorded in real time with out timelapse to get the period since I have no idea how to fix the time problem. I think fixing the time will also separate my data points by a lot graphically. I just worry about using a chart where in my lab report where only one axis is truly meaningful.

I know I can just explain the time problem in my error analysis but I am just wondering if anyone knows of a way to fix this? How can I convert my compressed timelapse time back to real time?

 

[haruspex]

This speed relative to time is 120x.

I don't understand… what is 120x what?

my data shows the total oscillation recording in about 25 seconds.

Are you saying one full cycle of oscillation takes about 25 seconds, so only about six frames? And that this makes it hard to determine the period accurately?

It is not clear exactly what the device gives you as data. As it just a video recording, in which case, taken from what angle? Or does it give some numerical output?
If you have angles at four second intervals, it is a matter of fitting a (decaying) sine curve to the data.

 

[hutchphd]

Homework Statement: Find the universal gravitational constant
Relevant Equations: F=Gm1m2/r

So my data shows the total oscillation recording in about 25 seconds.

You have a series of over 500 pictures. This is not sufficient data why?

 

[Steve4Physics]

@guyvsdcsniper, the problem is not clear. Do this help?...

The period of oscillation is (from distant memories) a number of minutes. So having a measurement-interval of 4.00s should be (more than) adequate..

You will need to go through the frames individually and manually read and record the position and time from each frame. Presumably your phone lets you step through individual frames. If you don’t know how to do this you need to find out!

If using all 600+ frames is too much work, consider using a frame-interval of, for example, 16s; you can always add missing frames later if required.

Of course, put the data into a spreadsheet as you read them and save regularly.

 

[guyvsdcsniper]

I don't understand… what is 120x what?

Are you saying one full cycle of oscillation takes about 25 seconds, so only about six frames? And that this makes it hard to determine the period accurately?

It is not clear exactly what the device gives you as data. As it just a video recording, in which case, taken from what angle? Or does it give some numerical output?
If you have angles at four second intervals, it is a matter of fitting a (decaying) sine curve to the data.

Sorry, i meant the speed of the video is 120x greater relative to real time.

To be more clear, I recorded the oscillation of the laser with at 1x speed, 1080p 30fps for an hour. Tracker tracks the laser's position as a function of a time, for every single individual frame for the whole hour. So when it plots the lasers position as a function of time, the time scale is ranges from 0 minutes to 1 hour. With this data, the period is 540 seconds.

I have also recorded the laser using a timelapse video, 1080p, 1 frame every 4 seconds for an hour. But because its a timelapse video, I will still get the same displacement as the regular video, but now the time interval is 0 seconds to about 35 seconds. So because the timelapse video compressed time, I cannot use this to accurately determine the period, because it gives a period of approximately 7 seconds.

So I am asking is there a way, knowing the fps of the timelapse video, to extract the true time that passed during the entire video, in order to accurately determine the period from that data.

 

[guyvsdcsniper]

@guyvsdcsniper, the problem is not clear. Do this help?...

The period of oscillation is (from distant memories) a number of minutes. So having a measurement-interval of 4.00s should be (more than) adequate..

You will need to go through the frames individually and manually read and record the position and time from each frame. Presumably your phone lets you step through individual frames. If you don’t know how to do this you need to find out!

If using all 600+ frames is too much work, consider using a frame-interval of, for example, 16s; you can always add missing frames later if required.

Of course, put the data into a spreadsheet as you read them and save regularly.

Hey, you can check my response above, I hope that makes my question more clear.

My phone does not let me go frame by frame unfortunately.

 

[haruspex]

i meant the speed of the video is 120x greater relative to real time.

I think you mean it is 120x faster than real time if played back at 30fps. It's not that the video itself is 120x real time. Why play it back so fast?

I recorded the oscillation of the laser with at 1x speed, 1080p

That's 1920 pixels across by 1080 vertically, right?

now the time interval is 0 seconds to about 35 seconds

Again, that is only if played back at the wrong speed, i.e. 120x too fast, no? And by interval you mean the whole recording, right?

With this data, the period is 540 seconds.

also recorded the laser using a timelapse video … it gives a period of approximately 7 seconds.

Now I am puzzled. If you play back at 120x real speed and observe a period of 7 seconds then the actual period should be about 840 seconds, not 540.
What about the number of oscillations? According to your statements, in the 30fps recording you saw about 7 cycles, but in the time lapse recording you only saw 4 or 5.

 

[hutchphd]

My phone does not let me go frame by frame unfortunately.

Does it produce a video file for each sequence? Can you view it with other software on, say, a computer? Is there guidance for this endeavor? What was the proposed procedure for the data extraction?

 

[Steve4Physics]

My phone does not let me go frame by frame unfortunately.

You can do it adequately without a frame-by-frame facility. Just manually 'freeze' at roughly equal time intervals. For each freeze:
- read and record the time;
- read and record the laser pointer's position.

You should end up with data (in a spreadsheet) which you can plot using software. The time intervals between consecutive points won't be exactly equal but that's not an issue.