1. ## Varaition!!

OK, I have a question here that's part of a homework task I have due tomorrow:

The time taken, t, for a pendulum to swing varies as the sqare root of its length, L. If one swing of a pendulum 98cm long takes 2 seconds, find the time taken for one swing of a pendulum 32cm long.

I know of varaition, direct variation etc, but what do I do in this case? I can't work it out.

Any help is greatly appreciated

2. Hello, corpse_bride!

The time $\displaystyle t$ for a pendulum to swing varies as the sqare root of its length $\displaystyle L.$
If one swing of a pendulum 98cm long takes 2 seconds,
find the time taken for one swing of a pendulum 32cm long.
This is direct variation . . .

Write the equation! . $\displaystyle t \;=\;k\sqrt{L}$

We are told: when $\displaystyle L = 98,\;t = 2$
. . So we have: .$\displaystyle 2 \;=\;k\sqrt{98}\quad\Rightarrow\quad k \:=\:\frac{2}{\sqrt{98}} \:=\:\frac{2}{7\sqrt{2}} \:=\:\frac{\sqrt{2}}{7}$
Hence: .$\displaystyle t \;=\;\frac{\sqrt{2}}{7}\sqrt{L}$

Now find $\displaystyle t$ when $\displaystyle L = 32.$

3. Originally Posted by corpse_bride
OK, I have a question here that's part of a homework task I have due tomorrow:

The time taken, t, for a pendulum to swing varies as the sqare root of its length, L. If one swing of a pendulum 98cm long takes 2 seconds, find the time taken for one swing of a pendulum 32cm long.

I know of varaition, direct variation etc, but what do I do in this case? I can't work it out.

Any help is greatly appreciated
we have $\displaystyle t = k\sqrt L$ from the given, we have $\displaystyle 2 = k \sqrt {98}$ or $\displaystyle k = \frac{2}{\sqrt {98}}$

using this for the second pendulum, we have $\displaystyle t = \frac{2\sqrt {32}}{\sqrt {98}} = 2 \sqrt{\frac{32}{98}} = (2) \left( {\frac{4}{7}} \right) \left( \sqrt 1 \right) = \frac{8}{7} \approx 1.142857.$