# Units of damping constant

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We've been given an equation for a damped pendulum which is A = A0 x e^-kn

Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and ln(A/cm) has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

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Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and ln(A/cm) has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

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#2

(Original post by

We've been given an equation for a damped pendulum which is A = A0 x e^-kn

Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and ln(A/cm) has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

Posted from TSR Mobile

**ambbs**)We've been given an equation for a damped pendulum which is A = A0 x e^-kn

Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and ln(A/cm) has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

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(Original post by

kn has to be dimensionless so if n is a number of swings, then k is 'per swing'.

**astro67**)kn has to be dimensionless so if n is a number of swings, then k is 'per swing'.

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#4

**ambbs**)

We've been given an equation for a damped pendulum which is A = A0 x e^-kn

Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and

**ln(A/cm)**has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

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ln cm

people who write physics books are imo bad at mentioning this - they probably came up using log graph paper which looks like this rather than doing it in excel or whatever

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(Original post by

it's the log of something that has units and you don't specify, how will people looking at the graph understand it?

ln cm

people who write physics books are imo bad at mentioning this - they probably came up using log graph paper which looks like this rather than doing it in excel or whatever

**Joinedup**)it's the log of something that has units and you don't specify, how will people looking at the graph understand it?

ln cm

people who write physics books are imo bad at mentioning this - they probably came up using log graph paper which looks like this rather than doing it in excel or whatever

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#6

**Joinedup**)

it's the log of something that has units and you don't specify, how will people looking at the graph understand it?

ln cm

people who write physics books are imo bad at mentioning this - they probably came up using log graph paper which looks like this rather than doing it in excel or whatever

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#7

**ambbs**)

We've been given an equation for a damped pendulum which is A = A0 x e^-kn

Where A is the amplitude in cm, A0 is the initial amplitude, k is the damping constant and n is number of swings.

I've collected results and plotted a graph of n against lnA - rearranging the equation gives lnA = -kn + lnA0, so k is the gradient of my graph.

N has no units and ln(A/cm) has no units, so it looks like k wouldn't have units either, but I can't help but think that k would have units - I'm just not sure what they are. I thought it could be per second, but I'm far from certain and none of my physics teachers seem to know. Thanks in advance to anyone who can shed some light on this!

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*constant*or damping

*coefficient*in physics usually relates to the damping force as it varies with the velocity of the moving object. What you have here is not usually referred to as the damping constant or coefficient, which, by the way could have units as determined by

F = kv (Or F=kv

^{2}possibly)

F being the damping force and v the velocity.

But as I say, this is not what we have here.

In the equation you have the constant k is a ratio. It would be called the logarithmic decrement, and is a measure of how much the amplitude of each successive swing decreases as a fraction of the previous amplitude.

As such this constant has no units and is dimensionless, as others have said here. It's a ratio.

If you want to look at it more closely you can see that from

You get

So if n is one oscillation, the value of k gives the log of the ratio of the amplitudes of two successive swings. To put some numbers in, if the amplitude of the 2nd swing was half the amplitude of the 1st

Gives k = 0.69

So k= 0.69 is the value of your constant, for example, for the amplitude to be halved each swing. This is actually quite severe damping for a pendulum. Your experimental values for k will be much less.

It has no unit. It needs no unit.

I hope this helps.

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**Stonebridge**)x

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#10

Thank you so much for this.In addition, could you please help me understand what the S.I unit of damping force would be?And if possible,The equation of damping co-efficient?Your response would be much appreciated!

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#11

(Original post by

Thank you so much for this.In addition, could you please help me understand what the S.I unit of damping force would be?And if possible,The equation of damping co-efficient?Your response would be much appreciated!

**Armaan Samani**)Thank you so much for this.In addition, could you please help me understand what the S.I unit of damping force would be?And if possible,The equation of damping co-efficient?Your response would be much appreciated!

I would make a reply to this post but I would not reply for subsequent questions. If you still have questions, start a new thread.

(Original post by

...In addition, could you please help me understand what the S.I unit of damping force would be?....

**Armaan Samani**)...In addition, could you please help me understand what the S.I unit of damping force would be?....

(Original post by

...And if possible,The equation of damping co-efficient? ...!

**Armaan Samani**)...And if possible,The equation of damping co-efficient? ...!

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

then the SI unit of the damping coefficient is

[tex] \dfrac{\text{N} \cdot \text{s} }{\text{kg} \cdot \text{m}}.

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