Finding Viscous Damping Constamt

[Trentonx]

Homework Statement

I am working with a problem of damped harmonic motion. I am given that the motion is in a medium that exerts a force of 2N when the speed is 4 cm/s. The mass is 5kg.

Homework Equations

C = F/v

The Attempt at a Solution

I thought that the viscous damping constant was given by:
C = F/v = (2N)/(.04m/s) = 50
But the book used C = (F*g)/v = 490

What is force times acceleration? It's not the mass, that's for sure. Is the book off here or am I?

 

[Nate810]

The book is correct. Force times acceleration is the same as force times gravitational acceleration, which is what they used in the equation. The equation for viscous damping constant is C = (F*g)/v, where F is the force exerted by the medium, g is the gravitational acceleration, and v is the speed.

 

[kerimek]

Your solution is correct, but it is important to note that there are different ways to calculate the viscous damping constant depending on the specific situation. The equation C = F/v is typically used when the force is constant and the velocity changes (such as in your problem), while the equation C = (F*g)/v is used when the force is proportional to the velocity (such as in the case of a falling object in air). Both equations are valid, so it is possible that the book is using a different scenario or simply made a mistake. It would be helpful to double check the context and equations used in the book to determine the reason for the discrepancy.