How to convert these equation to linear equation ?

In science subjects, Form 5 Bestari students conduct a simple pendulum experiment to determine the gravitational pull acceleration. The following table shows the results obtained from the experiment, The duration for a swing, #T#, a simple pendulum length l given by the equation. #T# = 2#pi# #sqrt(l/g)# , where #g# is the acceleration due to gravity pull.

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Change #T# = 2#pi# #sqrt(l/g)# to linear equation ...

1 Answer
Feb 12, 2018

It could be in two ways. See below for details.

Explanation:

First Method #-# As the relation is #T=2pisqrt(l/g)#, the relation between only two variables #l# and #T# is that

#Tpropsqrtl#

So if you draw a graph between #T# and #sqrtl#, it will be very close to a linear equation.

Second Method #-# We find such relation too often in physics, but it may be somewhat different. For example in place of #y=ksqrtx#, it may be #y^b=kx^a#

In such cases, it is better to take logarithm (to base #10#, say - as it is easily available from tables as well as calculators), and then it becomes

#alogy=blogx+logk#

Observe that the relation between #logy#and #logx# is linear. In above case we will have

#LogT=log((2pi)/sqrtg)=1/2logl#

which gives a linear relation between #logT# and #logl#