Question

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.

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

Answer 1

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`