Simple Pendulum: Explaining Why Time is Proportional to Route Length

[joshd]

hey people. i am new to these forums.

i am doing some coursework on pendulums, for science. i have collected results, and have of course found t is proportional to route length. for my analysis, i need to say WHY, using some scientific knowledge.

so why is it? also, why is t proportional to ROUTE l, rather than just plain old l?


thanks in advance

 

[Tide]

Here's one way to see the scaling. The change in potential energy of the pendulum bob as it oscillates is $m g L (1 - \cos \theta)$ which is approximately $m g L \theta^2/2$ for small angles. Similarly, the corresponding change in kinetic energy is $m v^2/2$. But $v = L \theta/ T$ where T is the period of the pendulum so the change in kinetic energy is about $m L^2 \theta^2 /T^2$.

Equating the two gives $L^2 /T^2 = g L$ from which T scales as $\sqrt {L/g}$.

 

[finchie_88]

lol, sounds like ur doing the same piece of coursework that I had to do about a week ago.

 

[joshd]

did you include that ^^^ in the analysis? i semi-understand it, lol.

what are the moderators wanting to get an 8 in the analysis strand?

 

[joshd]

right, i am now writing the analysis, and i do not know what to put.

i was going to say t is proportional to route l because when the pendulum is longer, the bob has got furthere to travel. but then i remembered that below 10 degrees, it doesn't matter what angle away from the vertical you set the pendulum swinging, it will always have the same period.

so why is it that t is proportional to route l??

 

[Tide]

so why is it that t is proportional to route l??

That question has already been answered. And, BTW, it is "root" and not "route."

 

[joshd]

well, my teacher says that is too complicated for a GCSE coursweork assignment. to get full marks on the analysis part of the mark scheme i need to:

using evidence collected, draw appropriate conclusions, and explain them using detailed scientific knowledge.

how can i explain what i found, in a more simple way that is not A level stuff. basically, what i need to know is why does it take longer for a longer length, if it is not the distance the bob has to travel? (in simple terms)

sorry if i have not been clear, or have been a bit stupid, i am only 15.

(ps, thanks for correcting me on the root spelling error)