Solve Oscillation Problem: Find C Value to Avoid Oscillations

[Petrulis]

Homework Statement

A spring (which tension is k) is connected with a body (which mass is m). The whole system is in viscous liquid. In this liquid frictional force is proportional to speed: F = -C*v. With what C value the oscillation won't happen?

The Attempt at a Solution

The damping ratio is defined as dr = c / (2 * sqrt(k * m)). No oscillation will happen when there is critical damping dr = 1 or when there is overdamping dr > 1.

So: C >= sqrt(4mk);

Is the solution above right?

 

[genneth]

The reasoning is correct, but I haven't checked your formulae.

 

[m2003]

Yes, the solution above is correct. The critical damping ratio is a measure of how much damping is needed to prevent oscillations in a system. In this context, the C value represents the damping coefficient, which is directly related to the damping ratio. By setting the damping ratio equal to 1, we can solve for the minimum value of C that will prevent oscillations. This minimum value is given by C >= sqrt(4mk), where m is the mass of the body and k is the spring constant. Any value of C that is equal to or greater than this minimum value will prevent oscillations from occurring in the system.