Pendulum

[Maverick56]

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Why is the graph of the relationship between period (T) and frequency (f) a parabola and not a straight line?

I know T= 1/f, so period and frequency are inversely proportional but what distinguishes this from a straight line graph?

 

[Gauss44]

Why is the graph of the relationship between period (T) and frequency (f) a parabola and not a straight line?

I know T= 1/f, so period and frequency are inversely proportional but what distinguishes this from a straight line graph?

Y=1/X is a curved line. Y=X or Y=-X would be straight lines because they are proportional, not inversely proportional.

The best answer here might explain it better: http://malaysia.answers.yahoo.com/question/index?qid=20100305043930AASA3EA

 

[asf503]

Straight lines share the generic equation:

y=mx+b

essentially, you can say that straight lines signify only proportional quantities, like a=b or a=(-b)

T=1/f is not a parabola, that needs to be understood now. A parabola is (essentially) in the form y=ax^n where n is any whole integer. Parabolas look like a U.

T=1/f is an inversely proportional relationship- and graphed in the form T=1/f, f can never be zero (or T will be infinity), which means T can never be 0 (since no value of f except infinity can make it zero). This is not how a line works, since any line would pass through 0 for one of the variables.

To answer your question in a sentence: Inversely proportional relationships never look like lines, because they can never have the generic form y=mx+b.