- #1

Ace.

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## Homework Statement

Show the unit analysis of this equation that relates frequency to length (in centimeters) of a pendulum

[itex]f = 5.1L^{-0.5}[/itex]

## Homework Equations

[itex]f = \frac{1}{2\pi\sqrt{\frac{L}{g}}} [/itex] ?

## The Attempt at a Solution

I cannot find much info about this online, but I gave it a go:

[itex]f = \frac{1}{2\pi\sqrt{\frac{L}{g}}}[/itex]

solving for L:

L = [itex]\frac{g}{2πf^{2}} * \frac{100 cm}{1 m}[/itex]

L = [itex]\frac{g}{f^{2}} * \frac{cm}{m}[/itex]

L = [itex]\frac{m/s^{2}}{(s^{-1})^{2}} * \frac{cm}{m}[/itex]

L = [itex]\frac{m}{s^{2}}* \frac{1}{s^{-2}} * \frac{cm}{m}[/itex]

L = [itex]cm[/itex][itex]f = \frac{1}{2\pi\sqrt{\frac{L}{g}}}[/itex]

[itex]f = \frac{1}{\sqrt{\frac{cm}{m/s^2} * \frac{m}{cm}}}[/itex]

[itex]f = \frac{1}{\sqrt{s^{2}}}[/itex]

[itex]f = s^{-1}[/itex]

Is this the right approach?