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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: f

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

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: f

_{osc}= .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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#2

(Original post by

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: f

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

**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: f

_{osc}= .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

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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(Original post by

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

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.

**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.

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**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.

_{osc}=

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(Original post by

Mg has units of force, and k force per metre....

**Pythononian**)Mg has units of force, and k force per metre....

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#8

On the rhs we have

mass - kg

g - ms

k - force per metre = Nm

so Nm

assume on the rhs the terms are [m]

so on the rhs we have

[kg]

on the left we have

s

Find the values of a b and c that balance the equation so that there is s

mass - kg

g - ms

^{-2}k - force per metre = Nm

^{-1}and N = kgms^{-2}from F=maso Nm

^{-1}is kgms^{-2}m^{-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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(Original post by

On the rhs we have

mass - kg

g - ms

k - force per metre = Nm

so Nm

assume on the rhs the terms are [m]

so on the rhs we have

[kg]

on the left we have

s

Find the values of a b and c that balance the equation so that there is s

**Stonebridge**)On the rhs we have

mass - kg

g - ms

^{-2}k - force per metre = Nm

^{-1}and N = kgms^{-2}from F=maso Nm

^{-1}is kgms^{-2}m^{-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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#10

(Original post by

Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?

**3 Phase Duck**)Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?

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 = m

^{a}g

^{b}k

^{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

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(Original post by

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 = m

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

**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 = m

^{a}g^{b}k^{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

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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