3 Phase Duck
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This question is in relation to Hookes law and angular frequency (I think).

Q. Use the principle of dimensional homogeniety to deduce an expression for the frequency of oscillation in terms of stiffness (k), the mass (m) and the gravitational cosntant (g).

My answer is: fosc= \frac{k-g}{m}.

Is this right?


Sorry I do elec eng so I don't do this kind of physics very often but there's going to be something similar in one of my exams tomorrow, so any help would be great. Cheers
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Stonebridge
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(Original post by 3 Phase Duck)
This question is in relation to Hookes law and angular frequency (I think).

Q. Use the principle of dimensional homogeniety to deduce an expression for the frequency of oscillation in terms of stiffness (k), the mass (m) and the gravitational cosntant (g).

My answer is: fosc= \frac{k-g}{m}.

Is this right?


Sorry I do elec eng so I don't do this kind of physics very often but there's going to be something similar in one of my exams tomorrow, so any help would be great. Cheers
How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
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3 Phase Duck
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(Original post by Stonebridge)
How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
Ahh right, ok. I'll give it a shot.
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3 Phase Duck
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(Original post by Stonebridge)
How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
Ok so would it just be fosc=\sqrt{\frac{k}{gm}}
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Pythononian
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(Original post by 3 Phase Duck)
Ok so would it just be fosc=\sqrt{\frac{k}{gm}}
Mg has units of force, and k force per metre....
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3 Phase Duck
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(Original post by Pythononian)
Mg has units of force, and k force per metre....
Tbh I'm unsure where g comes into it really.
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3 Phase Duck
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I'm confused here. mg (as in small g, the acceleration due to gravity) = -kx.

and

\omega = \sqrt{\frac{k}{m}}

But where does the gravitational constant come into it?
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Stonebridge
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On the rhs we have
mass - kg
g - ms-2
k - force per metre = Nm-1 and N = kgms-2 from F=ma
so Nm-1 is kgms-2m-1

assume on the rhs the terms are [m]a[g]b[k]c
so on the rhs we have
[kg]a[ms-2]b[kgs-2]c
on the left we have
s-1

Find the values of a b and c that balance the equation so that there is s-1 on both sides
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3 Phase Duck
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(Original post by Stonebridge)
On the rhs we have
mass - kg
g - ms-2
k - force per metre = Nm-1 and N = kgms-2 from F=ma
so Nm-1 is kgms-2m-1

assume on the rhs the terms are [m]a[g]b[k]c
so on the rhs we have
[kg]a[ms-2]b[kgs-2]c
on the left we have
s-1

Find the values of a b and c that balance the equation so that there is s-1 on both sides
Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?
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Stonebridge
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(Original post by 3 Phase Duck)
Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?
No,because, for a start, b must be zero.
I can see that you haven't done an example of (or been taught?) dimensional analysis. It's a bit difficult to teach you it here from scratch.
This is how it's done. I suggest you find some notes on this (Google it) and study them.

We have
f = magbkc
[s]^{-1} = [kg]^a[ms^{-2}]^b[kgs^{-2}]^c

balancing for m gives b=0 as there is no m term on the left

looking at kg gives
0 = a + c -------(1)

looking at s gives
-1 = -2b -2c
which gives
-1 = -2c as b=0
So
c = ½

and subbing back in (1)
a = -½

This gives the formula as
f = \sqrt{\frac{k}{m}}
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3 Phase Duck
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(Original post by Stonebridge)
No,because, for a start, b must be zero.
I can see that you haven't done an example of (or been taught?) dimensional analysis. It's a bit difficult to teach you it here from scratch.
This is how it's done. I suggest you find some notes on this (Google it) and study them.

We have
f = magbkc
[s]^1 = [kg]^a[ms^{-2}]^b[kgs^{-2}]^c

balancing for m gives b=0 as there is no m term on the left

looking at kg gives
0 = a + c -------(1)

looking at s gives
-1 = -2b -2c
which gives
-1 = -2c as b=0
So
c = ½

and subbing back in (1)
a = -½

This gives the formula as
f = \sqrt{\frac{k}{m}}
Cheers, we haven't been taught because we are supposed to know this already. However I've never done A-level physics so this is quite new to me.

Thanks anyway, it actually makes more sense when you explain it like that. I was getting confused because of b and where G lies in all of this.
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