Question

Help and explain? Please?

A pendulum L inches in length takes t seconds to make one full cycle according to the equation

t = 2π√L / 384


To the nearest tenth of an inch, what is the length of a pendulum that completes one full cycle every 1.5 seconds?

Answer 1

The easiest way to do this type of problem is to first rearrange the equation with the variable you want on one side, and everything else on the other, so in this case you're going to want to get the variable L by its self!

Answer 2

How do I get L by itself? It's in the square root sign.

Answer 3

Well first can you get everything else to the other side so you just have sqrt of L?

Answer 4

Okay, so first do I get rid of the 384? I think you times it by T.

Answer 5

Right! So you've gotten that to the other side, now how would you move the 2 pi

Answer 6

Minus 2 pi?

Answer 7

Not quite! Because the sqrt t and 2 pi are multiplied, you would have divide by two pi on both sides of the equation!
\[\sqrt{L} = \frac{384 t}{2 \pi}\]
Now, how to get rid of the square root? What's the opposite of it?

Answer 8

Oh, I understand now! So would you square both sides?

Answer 9

Exactly!
\[L = (\frac{384 t}{2 \pi })^{2}\]
Now just plug in the value of t, and plug and chug!

Answer 10

I plug t in and I'm not getting the right answer. Am I doing something wrong?

Answer 11

T would be 1.5.

Answer 12

\[L = (\frac{384 (1.5)}{2 \pi})^{2} = 8404.0\]

Answer 13

Same thing I got!

Answer 14

Sadly, none of the answer choices. :(

Answer 15

(21.9) (9.6) (14.6) or (29.2)? I wonder what I did wrong.

Answer 16

OH it said to the "nearest tenth of an inch" does that have something to do with it?

Answer 17

Was the 384 also under a square root?

Answer 18

Yes, 384 and L.

Answer 19

Oh! I'm sorry, well then that changes it a bit! I'm sorry! I didn't think they would have given you it as a constant under it...so, we would have done all of the same things, when we moved the 384 it was under a square root so the equation was really...
\[L = (\frac{\sqrt{384} t}{2 \pi})^{2}\] but only the 384 is under the sqare root! this should you give you the answer 21.9 approximately!

Answer 20

Ohhhh, sorry for not telling you! It's fine, and I understand it now. Thanks you helped alot! :)