Plotting the graph of pendulum period versus length

[Revin]

why do we square the value of T ( time period) while plotting the graph of effect on time period of a pendulum with change in its effective length ?

also while deriving the formula of
T=2∏√(l/g)

why do we take T^2 = 1/g.

Whats the need for squaring the time period ?

 

[Muthumanimaran]

Because for the convenience. even if you don't square Timeperiod nothing will change, you will always get a parabola with T>0 and l>0

 

[jtbell]

To get a straight-line graph, you can plot either T² versus l, or T versus √l. If your calculator doesn't have a square-root key, the first method is easier.

 

[bhillyard]

More generally if you are trying to identify the relationship between two quantities it is difficult to look at a curve and say it is an arc of a circle, parabola, hyperbola, exponential or whatever. However it is much easier to recognise a straight line. So we transform the equation to produce a linear relationship. In this case squaring the equation gives a straight line by plotting t² against l.
This gives a straight line whose gradient would be is 4∏²/g.

 

[PJC01]

When plotting the graph of pendulum period versus length, we square the value of T (time period) because it allows us to have a linear relationship between the two variables. This makes it easier to analyze and interpret the data.

In terms of deriving the formula for the period of a pendulum, we take T^2 = 1/g because it helps us to isolate the variable we are interested in (length) and see its direct relationship with the period. By squaring both sides of the equation, we are able to eliminate the square root and have a simpler expression that clearly shows the relationship between the two variables.

The need for squaring the time period in both cases is to simplify the equation and make it easier to understand and use. It also allows us to see the direct relationship between the variables without any additional calculations or manipulations. Additionally, squaring the time period helps to eliminate any negative values that may arise from taking the square root of g in the formula. Overall, squaring the time period allows for a more straightforward and accurate interpretation of the data and formula.