- #1

llstanfield

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Beginning student striving to learn. The problem was generated by people from the University of Winnipeg. Source: http://theory.uwinnipeg.ca/physics/ (this website was actually suggested by a user on the forums who suggested utilizing it as a learning source).

Problem is, quote:

The period of a simple pendulum, defined as the time for one complete oscillation, is measured in time units and is given by:

T = 2∏√l/g

where,l is the length of the pendulum and g is the acceleration due to gravity,

The solution is actually given. The full equation was as follows:

[2∏√l/g]= √L/L/t

Given the description which is italicized, I understood how they got: √L/L/t

My attempt: The italicized description already tells us that "g"= L/t

I've thought about it for several minutes, and I still can't understand how to mathematically describe T and the aforementioned equation including 2∏. Can anyone help? Thank you for your time.

## Homework Statement

Problem is, quote:

The period of a simple pendulum, defined as the time for one complete oscillation, is measured in time units and is given by:

T = 2∏√l/g

where,l is the length of the pendulum and g is the acceleration due to gravity,

*in units of length divided by time squared.*Show that this equation is dimensionally consistent; that is, show that the right hand side of this equation gives units of time.## Homework Equations

The solution is actually given. The full equation was as follows:

[2∏√l/g]= √L/L/t

^{2}. This all equals: √t^{2}which = T## The Attempt at a Solution

Given the description which is italicized, I understood how they got: √L/L/t

^{2}which ultimately equals T, but I do not understand how "2∏" disappeared so easily in the process of equating T.My attempt: The italicized description already tells us that "g"= L/t

^{2}. Given this information, dividing "L" by L/t^{2}will result in t^{2}(all under the square root symbol). Then, the √t^{2}is T. I get stuck on the conversion process when it comes to 2∏ however.I've thought about it for several minutes, and I still can't understand how to mathematically describe T and the aforementioned equation including 2∏. Can anyone help? Thank you for your time.

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