
Title:
0758 Finding Simple Harmonic Motion

Description:

Okay, let's see. We want a period of 1 second.

Let's convert this to an angular frequency ω using this equation.

So, we want an angular frequency of 2π, an I know that ω²

is equal to whatever this thing is, the minus something times x.

In this case, ω² is equal to g/L. Let's solve this for L.

This gives me a length of 0.25 meters.

Now, it turns out that for pendulum clocks, actually, we might want a period of 2 seconds.

The reason is because let's say we had a pendulum with a period of 1 second.

That means that it takes 1 second for when I pull it back to go

over here and then all the way back.

That's actually quite a bit of motion and a period of 2 seconds is actually a little bit better,

because then every time the pendulum reaches one if its extrema,

either all the way over here or all the way over there,

we know 1 second has passedhalf of the period.

I wonder what would be the period for a 2second pendulum.

Why don't ask Tjeerd the clockmaker what he thinks.

[Tjeerd ] When you design a pendulum or pendulum clock,

the thing that mostly influences the period of oscillation is the length of the your pendulum.

If you have an ideal pendulum, a fictional pendulum,

made out of no materials as a mathematical piece,

the pendulum of a second, oscillating in a second,

will have a length of about a meter.

A pendulum is made out of materials, and the rod, for instance, is made out of steel or brass,

which brings the center of oscillation up.

That's why you need a heavy pendulum bulb underneath the pendulum

to bring the center of gravity in the pendulum down

to have your proper theoretical length.