SHM: What Factors Affect the Period of a Pendulum?

[jimmy p]

SHM - easy question!

Hi i know that this is probably an extremely easy and obvious question, but we are looking at pendulums in A2 physics and i was just wondering if there are any other factors affecting the period of a pendulum other than these:

- Length of string
- Mass of pendulum
- Shape of pendulum

Im not sure of angle of swing i assumed that any change in period would be negligible if the above factors are constant, but if I am wrong feel free to correct me and if there are any more, please add to my list!

thanx

 

[FZ+]

Yes to angle of swing.

The SHM model of the unforced, damped pendulum makes the assumption that the equation is linear, approximating
t'' + yt' + asin t = 0

to:

t'' + yt' + at = 0

Which only works out at small amplitudes, where sin t -> t

In general, shape (unless we are talking air resistance), and mass shouldn't affect the period, IIRC. Length from pivot to centre of mass is the big one.

 

[quantumdude]

Yes to the shape of the pendulum as well. That differential equation assumes that the mass is a point mass on a massless rod. If we relax that assumption, then we must take into account the rotational inertia of the pendulum, which in general is not the same as that of a point mass. The rotational inertia is a geometrical factor.

More on this here:
http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

 

[jimmy p]

Ok so the factors that effect a pendulum are:

- Length of rod
- Mass of Pendulum
- Angle of Swing
- Shape of Pendulum

Or am i missing the point here Also what are the equations that link these together or does each separate variable have its own equation...ooh are there any constants?

thanx

 

[HallsofIvy]

Depends upon exactly what you are looking at.

In general, mass is not important in gravitational problems. If you are including air resistance, then it might be important (actually density more than mass alone).

Shape, again assuming no air resistance, affects the position of the center of gravity. If you allow for that by taking the center of gravity as the "end" of the pendulum- i.e. measure length to the center of gravity, you can then ignore the shape. With air resistance then the shape is very important- different shapes will intecept the air differently.

"Angle of pendulum"- I assume you mean the initial angle- will affect the height on both sides but not the period.

Length of the pendulum is the most important. The period of the pendulum is approximately proportional to the length.

One thing you have not listed and certainly should is friction at the pivot! Everything I said above is assuming no friction. If there is friction then the motion is not periodic and will eventually halt.

 

[jimmy p]

ok

All right then, that has helped, i looked smart in my physics lesson today so i owe u guys one! lol. I am guessing that the reason our experimental periods took longer than the ones we worked out using the equation T = 2π * root(l/g) was due to air resistance and friction lol...

 

[HallsofIvy]

I've always advocated removing all the air from physics laboratories!

 

[ranyart]

Originally posted by jimmy p
All right then, that has helped, i looked smart in my physics lesson today so i owe u guys one! lol. I am guessing that the reason our experimental periods took longer than the ones we worked out using the equation T = 2π * root(l/g) was due to air resistance and friction lol...

You can really elevate your status in class to above shoulder height, if you go back and ask your teacher to transfer the original pendulum inquiries from: A three dimensional object(pendulum/rod) oscillating in a three dimensional space) which produces all the factors of physical properties provided in the link of Tom:http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

All the properties relate to interactions and movement in a 4-dimensional spacetime.

Now if you use a 'rod' of energy instead of the pendulum that restricts its movements to 2-dimensions only, you can replace the 'rod' with Electro-Magnetic energy of the Photon, then you get a dimensional dispersion, from two dimensional(E-M) to a zero point, 1-dimensional!

The original pendulum can transmit its quantities in a variaty of ways, its dispersion is through inter-connecting 4-dimensional spacetime, which allows collisions to occur, so you can follow one quantity for action-reactions. Reducing a pendulum from a physical three dimensional object, to one that is a two-dimensional entity, produces a Quantum leap for interactions( all interactions are not within a three-dimensional space-time so do not get observed)here:http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html#c3

 

[jimmy p]

Well at the moment i am at the top AND bottom of the class. There are only two ppl doing A2 physics in my college and the other dude is ill and has been for a while how poo is that huh? but at least the tutor is teaching me new stuff instead of waiting which is cool. No point in thwarting my learning cos my physics-buddy has a weak immune system.

 

[jimmy p]

Oh yeah, i forgot to say thanks for all ur help guys!