Calculating Viscous Damper Energy in Spring-Mass Systems

[physea]

Hello,

In problems that involve springs and viscous dampers, eg a mass falls on a spring that also has a viscous damper, how can we calculate the energy absorbed by the damper?

I mean, we know the energy absorbed by the spring (1/2*k*x^2), we know the kinetic energy of the mass (1/2*m*u^2), but what is the energy absorbed by the damper?

thanks

 

[Chestermiller]

If there were no viscous damping, what would be the change in the sum of kinetic energy of the mass and elastic energy stored in the spring?

 

[physea]

If there were no viscous damping, what would be the change in the sum of kinetic energy of the mass and elastic energy stored in the spring?

Zero

 

[Chestermiller]

So what does that tell you about the change in the sum of kinetic energy of the mass and elastic energy stored in the spring if there is viscous damping also present?

 

[physea]

So what does that tell you about the change in the sum of kinetic energy of the mass and elastic energy stored in the spring if there is viscous damping also present?

Zero again, we wasted all that time and these posts to check if energy conservation still applies to systems with dampers? Ofcourse it does but you have not addressed my question: what is the equation for the damper energy absorption?

 

[Chestermiller]

Zero again, we wasted all that time and these posts to check if energy conservation still applies to systems with dampers? Ofcourse it does but you have not addressed my question: what is the equation for the damper energy absorption?

The answer is not zero when viscous damping is present. So, do you still feel I wasted your time?

 

[physea]

The answer is not zero when viscous damping is present.

The energy lost in the damper and the energy stored in the spring equals to the kinetic energy of the mass. But you do not answer my question.
I don't want to calculate the damper energy indirectly, via the kinetic energy of the mass and the spring energy. I want to calculate it DIRECTLY with an equation.

 

[Chestermiller]

The energy lost in the damper and the energy stored in the spring equals to the kinetic energy of the mass. But you do not answer my question.
I don't want to calculate the damper energy indirectly, via the kinetic energy of the mass and the spring energy. I want to calculate it DIRECTLY with an equation.

The change in kinetic energy plus the change in stored elastic energy is equal to minus the energy dissipated in the damper.

 

[sophiecentaur]

Zero again, we wasted all that time and these posts to check if energy conservation still applies to systems with dampers? Ofcourse it does but you have not addressed my question: what is the equation for the damper energy absorption?

A little more politeness would be in order, I think. The customer is only always right when they are actually paying money for a service. Play nicely!

 

[Chestermiller]

A little more politeness would be in order, I think. The customer is only always right when they are actually paying money for a service. Play nicely!

Whoever said “the customer is always right” has never met the customer.

 

[Chestermiller]

But you do not answer my question.
I don't want to calculate the damper energy indirectly, via the kinetic energy of the mass and the spring energy. I want to calculate it DIRECTLY with an equation.

Well, based on your posts up to now, how could I possibly have guessed that this is what you wanted? Do you think I can read your mind? If you want to calculate the energy dissipated by the damper DIRECTLY, then you can use this equation:
$$E=C\int_0^t{v^2}dt$$where C is the damper constant, t is the elapsed time, and v is the velocity difference between the ends of the damper.

 

[physea]

Well, based on your posts up to now, how could I possibly have guessed that this is what you wanted? Do you think I can read your mind? If you want to calculate the energy dissipated by the damper DIRECTLY, then you can use this equation:
$$E=C\int_0^t{v^2}dt$$where C is the damper constant, t is the elapsed time, and v is the velocity difference between the ends of the damper.

Yeah, that's what I wanted thanks.

Btw, I derived it on my own like this:
F=cV (force of the damper)
So W=Fdx=c(Vdx)
We know that dx=Vdt
So W=c(V^2dt)

But I see some other equations like W=1/2c*dV*dx

Which is correct? I know this is maths, but I am not sure how to derive it myself.

 

[Chestermiller]

Yeah, that's what I wanted thanks.

Btw, I derived it on my own like this:
F=cV (force of the damper)
So W=Fdx=c(Vdx)
We know that dx=Vdt
So W=c(V^2dt)

But I see some other equations like W=1/2c*dV*dx

Which is correct? I know this is maths, but I am not sure how to derive it myself.

Your derivation is correct.

 

[physea]

Your derivation is correct.

So W=c(V^2dt) is correct
and W=1/2c*dV*dx is not correct?

If both are correct, how do we go from the first to the second?

 

[Chestermiller]

So W=c(V^2dt) is correct
and W=1/2c*dV*dx is not correct?

If both are correct, how do we go from the first to the second?

The first one should be an integral with respect to t. Otherwise you have a finite quantity equated to a differential. The second one makes no sense to me. To demonstrate that the first one is correct, obtain the dissipated damper energy from this equation , and then compare it with the change in the sum of kinetic- and elastic potential energy.

 

[Mister T]

The energy lost in the damper and the energy stored in the spring equals to the kinetic energy of the mass. But you do not answer my question.
I don't want to calculate the damper energy indirectly, via the kinetic energy of the mass and the spring energy. I want to calculate it DIRECTLY with an equation.

The damper converts mechanical energy to thermal energy. You would need to measure things like temperature changes of the internal components of the damper and relate those to the increase in thermal energy of those components. (Often authors will use the term internal energy rather than thermal energy.)