Why can't I stop playing this game (Angry Birds). I think these 'physics' games where you never really know what will happen are appealing to me.
So, I was playing the recent Angry Birds Seasons Valentines level and I noticed something cool. They have these 'cupid' pigs that are swinging from invisible ropes. Here is a video (could be a spoiler if haven't played this level yet - you have been warned).
Questions:
- Does this cupid-pig move like a realistic pendulum?
- If the above answer is yes, then does the gravitational field for that motion match with the projectile birds?
- Does this motion fall under the small-angle approximation?
Let's get to work. First, from my previous analysis of Angry Birds, I found that the sling shot shooter was 4.9 meters tall (assuming Earth-like gravity). Using that, here is a plot of one of the swinging bird. (of course this is from the Tracker Video analysis tool)
If I fit a sinusoidal function to this data, I get:
This sure looks like simple harmonic motion (which is what you should get for an oscillating mass with a small angular amplitude). Quick note. Everyone seems to think that pendulum motion is child's play. It must be - it is in the intro textbooks, right? I don't think it is quite that simple. This is probably more info than you wanted on pendulums - but just in case.
What useful information can I get out of that fit? The angular frequency is going to be useful. From above, you can see that the angular frequency is 0.582 rad/s. For a pendulum, this is related to the length (or Radius) and the gravitational field (g). This means that:
Here I will assume an Earth-like g. This will give a pendulum with a length of:
Remember, that assumes that I already know g. What angular amplitude would that have? Well, if the length is 29 meters and the x-amplitude is around 6 meters, this would make a maximum angle of:
This is about 12 degrees and should be small enough for the 'small-angle approximation'.
I tried to get my y oscillation data to work out, but it seems there was a problem. I had decided to make my own video since the ones posted on youtube weren't the best quality. During this videoing, I don't think the camera was stable enough. Since the vertical oscillation is so small, this shaking had a bigger effect.
In the end, it seems that the Angry Birds game does indeed have the flying pigs on strings. See, I knew there was a trick. Also, it goes to show that in many games it is easier to just put realistic physics in there to make things work.
Now, back to Angry Birds. I have to finish these Valentines levels before they come out with a Mardi Gras edition.
