Why would knowing the pendulum length required for a period of one second be useful ?

Answer 1

Let's at first find out, what should be the length of ta one second pendulum. For mathematical pendulum we can use the formula

T = 2π√(l/g),

where

l - length of the pendulum,

g - acceleration of gravitational attraction,

π = 3.14 - is the ration of the circumference to the radius.

If we square the left and right part, we get

T² =4π²l/g

From here length of the pendulum

l = gT² / 4π²

Now to simplify mathematical calculations I will use the fact that

g ≡ π²

It means that their numerical values are equal, of course don't forget that acceleration of free fall g has units m / s².

Now we see that

l = T² / 4,

it means that if the length of the pendulum is 25 cm, its period of oscillations is 1 second!

My congratulations! WE INVENTED THE CLOCK.

Ooops, It is Huygens and Galileo. Anyway we were close...

It is useful to draw the graph that is showing how the displacement depends on time and amplitude of the oscillations. From the graph it could be seen when the pendulum is reaching maximum displacement, when it is going through equilibrium position and so on. What is important: it is repetitive or periodic motion!

It is amazing that for the small angles the period of oscillations of pendulum does not depend on mass and amplitude of oscillations. The first man who discovered it - Galileo Galilei, who brought experiment to physics. He was using the bits of his own pulse and found out, that the chandeliers in the cathedral where he was present, were swinging because of the wind with the same period although their masses were different.

Physics is an excited science and I want all of you invest more time to understand its beauty and importance to the modern world.