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# Simple pendulum equation (logs) watch

1. Someone has asked a similar question before but the working was missing. The equation for a simple pendulum is:

T = 2pi sqrt(L/g)

I need to take logs of both sides to calculate g, apparently it should be:

log t = log ( 2 pi sqrt g) + log sqrt L

Is this correct and can you show step-by-step how to get to this(the answer is given on another thread)? The part I'm struggling to understand is how you separate sqrt L from its original place.
2. (Original post by pine444apple)
Someone has asked a similar question before but the working was missing. The equation for a simple pendulum is:

T = 2pi sqrt(L/g)

I need to take logs of both sides to calculate g, apparently it should be:

log t = log ( 2 pi sqrt g) + log sqrt L

Is this correct and can you show step-by-step how to get to this(the answer is given on another thread)? The part I'm struggling to understand is how you separate sqrt L from its original place.
You dont need to take logs if you’re trying to arrange for g.
3. (Original post by RDKGames)
You dont need to take logs if you’re trying to arrange for g.
Thanks but I didn't say that. I'll be calculating g at a later stage, so yes at this stage I absolutely do need to take logs, that's all I was asking help with.
4. (Original post by pine444apple)
Thanks but I didn't say that. I'll be calculating g at a later stage, so yes at this stage I absolutely do need to take logs, that's all I was asking help with.
Well then I'm not sure what you're asking for.

You said "I need to take logs of both sides to calculate g" which is not true.

5. [QUOTE=RDKGames;76532944]Well then I'm not sure what you're asking for.

I'll try again. I need to take logs of both sides of this equation, that's all.

Can you show me how?
6. (Original post by pine444apple)
Someone has asked a similar question before but the working was missing. The equation for a simple pendulum is:

T = 2pi sqrt(L/g)

I need to take logs of both sides to calculate g, apparently it should be:

log t = log ( 2 pi sqrt g) + log sqrt L

Is this correct and can you show step-by-step how to get to this(the answer is given on another thread)? The part I'm struggling to understand is how you separate sqrt L from its original place.
It needs to be log(2pi/sqrt(g)) rather than log(2pisqrt(g)), when taking the logarithm you just use log(a)+log(b)=log(ab) and the other property log(a^n)=nlog(a) may also prove useful if you want to get rid of the sqrts.

There seems to be some confusion as to why you are taking logarithms. The only reason I can see why you would want to do that is if this a Physics experimental data question where you have data for T and for L and are trying to use this to calculate g by plotting a straight line and finding the intercept.

However, if this is the case this should really be in the Physics section rather than the Maths section.

If you want to calculate g from just one result for T and L rather than lots of experimental data then you simply square both sides and rearrange for g and plug in the value of T and L.
7. (Original post by Dalek1099)
if this a Physics experimental data question where you have data for T and for L and are trying to use this to calculate g by plotting a straight line and finding the intercept.
This is it, I should have been more clear about that, although it's in my Maths A-level unit for some reason.

It needs to be log(2pi/sqrt(g)) rather than log(2pisqrt(g)), when taking the logarithm you just use log(a)+log(b)=log(ab) and the other property log(a^n)=nlog(a) may also prove useful if you want to get rid of the sqrts.
So step-by-step it should be something like:

At this stage you're saying I move the like this:

Which is almost in the form ?
8. (Original post by pine444apple)
This is it, I should have been more clear about that, although it's in my Maths A-level unit for some reason.

So step-by-step it should be something like:

At this stage you're saying I move the like this:

Which is almost in the form ?
It pretty much is of that form. log(T) is your y, log(2pi/root g) is your c, 1/2 is your m, and log(L) is your x.

If that's what you're trying to achieve.
9. (Original post by pine444apple)
This is it, I should have been more clear about that, although it's in my Maths A-level unit for some reason.

So step-by-step it should be something like:

At this stage you're saying I move the like this:

Which is almost in the form ?
This is in the form y=mx+c where y=log(T),m=1/2,x=log(L) and c=log(2pi/sqrt(g)). When doing this your y and x will always be the logarithm of the variables of the experimental data or potentially proportional to the logarithm but that doesn't really matter like you could choose m=1 and x=1/2log(L) for example but it wouldn't make a difference to your calculations as long as you draw the graph based on how you've written it in the form y=mx+c.

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