- Good morning.
Billy, Bobby, Bo, it is nice to have you back again.
- Yeah. Thanks Mr. P. It was weird to be absent from class so much.
- Yeah. - Right.
Flipping Physics
- Bo, remind me, what is the definition of the period of simple harmonic motion and, what is its symbol?
- The symbol for period is t …
- Capital T. - Capital T.
The period is the time it takes for one full oscillation or cycle of simple harmonic motion.
- Why is the symbol for period capital T?
Shouldn't it be P for period?
- P is for power.
- Actually capital P is for power,
lowercase p is for momentum; perhaps, it is because the Latin word for time is “Tempus”,
hence, capital T. You know, like “Tempus Fugit”, Time flies?
- Okay. - Eh.
- I'm in the Latin club!
- Sure, it could be capital T for Tempus, I don't actually know if it is or not, but sure!
Frequency or lowercase f is defined as the number of cycles per second.
That means frequency and period are inverses of one another.
- Oh, right, because period is in seconds per cycle and frequency is in cycles per second.
So if you take the inverse of one, you get the other. That makes sense!
Cycles per second are called Hertz or Hz which are named after the 19th century German physicist
Heinrich Hertz who is the first to give conclusive proof of the existence of electromagnetic waves
which were theorized by James Clerk Maxwell's electromagnetic theory of light
which we will learn about later.
Now, let's look at an example of a mass spring system that has a period of 0.77 seconds.
Bobby, could you please determine its frequency?
- Well, frequency and period are inverses of one another, so
frequency equals one over period or one divided by 0.77 which is 1.2987 or with two significant digits 1.3 …
cycles per second or hertz.
- Good. Okay, please watch as the mass goes through 1.3 cycles in one second.
- That’s really hard to see. - Yeah, how do we know that is 1.3 cycles?
- That would be the same as 6.5 cycles in five seconds,
and it's a whole lot easier to see when it's gone through half a cycle than 0.3 cycles.
- What? - Yeah, what?
- Multiply frequency by 5 over 5,
which is just 1 and you can multiply any number by 1 because it does not change the number.
1.3 times 5 is 6.5 and therefore we get 6.5 cycles in 5 seconds.
- Oh. - Okay, sure!
- It's a good point Bo.
If we watch for 5 seconds,
we get more easily see that the mass-spring system has gone through six and a half cycles.
Okay, let's do another example.
This pendulum goes through 15 cycles in 11 seconds. Billy, what is the frequency of this pendulum?
- Well, frequency is in cycles per second.
So, we just divide 15 cycles by 11 seconds to get 1.36 with the 36 repeating, or
1.4 cycles per second with 2 significant digits.
Actually, do you want the units as cycles per second or Hertz?
- That is like asking if I would prefer watts or joules per second.
They are the same!
Cycles per second and Hertz are the same, so I do not really care which units you give your answer.
However, it is very important that you remember that Hertz are cycles per second.
Notice this means we can determine the period of the pendulum.
It is 0.73 seconds.
Thank you very much for learning with me today.
I enjoyed learning with you.