[MUSIC]
Well, this short session is on vibration, but
it's specifically to do with transmissibility.
Wonderful mosaic we're going to come across
in terms of vibration control is one to do with transmissibility.
And it's one linked to something called vibration isolation.
So t in this case represents the amount of transmission of
vibration from source to reception.
And it's basically a function of the driving frequency of the vibration and
of the resonant frequency of the mass-spring system.
So in this particular case, there are two expressions that we can use.
The first one, I'm writing it down.
Basically has this formula where the f of f naught square
is taken away from the bottom.
This is for situations where the f is greater than f naught.
So in this particular formula here, the f naught is the resonant frequency, or
natural frequency of the system, and f is the driving frequency.
The other format you can have, okay, is when f is less than f naught.
And the only real difference with this is that the transmissibility
this time is 1 minus f over f naught squared, okay?
To know why there's a difference, you need to look at the actual notes that I
cover to explain that in a little more detail.
In this particular tutorial, I'm gonna take this first formula, and
what we're gonna do is look at rearranging that formula for f naught.
Again, I'm doing this because this is a very, very popular exam question
in both the general acoustics paper, and the noise control paper.
So it's a particular important maths to do, so
when you use this formula here, okay, and we're gonna rearrange that formula for
f naught which is a natural frequency of the source.
So the first thing to do is I'm gonna take this term here and put it to the top and
take the t and put that at the bottom.
So the first stage is to end up with f of f naught
squared minus 1 equals 1 divided by 2,
so all I've done is switch these two terms, okay?
That's all we've done there.
So we've got the f naught, it's tied in here.
There's a minus 1 there.
Well, let's just basically take that minus 1 across,
and it comes plus 1 on this side.
Okay, so we end up with that.
We might as well now square this out, so
this becomes f squared of f naught squared equals all that.
Okay, so we've just squared that out.
The f naught squared is tied up in the division sum here.
So what we can do now,
put a bracket round that cuz I'm gonna switch these two terms around.
So the f square stays where it is, the f naught squared goes to the top, and
this term here, the 1 over t plus 1, goes to the bottom.
Now when you get to that stage,
you've probably already keyed in some numbers into the formula.
So this particular denominator here won't look as clumsy as what it is here, okay?
So we've given the t value and that will be a single figure.
To make this into simply f naught,
we just take the square root of this term, okay?
So basically all we do is square root both sides and we ended with that.
So as I said, this is a very common manipulation that you need to do,
particularly in the exam situation.
The only thing that you often have to do is to rearrange it for f as well, okay?
So again it's a similar process but
obviously we go our separate ways when we get to this stage here.
Okay, so that concludes that brief tutorial.