# Problem of harmonic motion

## Homework Statement

A particle with mass m is undergoing with harmonic motion with a period T, we introduce an external force F proportional to velocity v so that F= -bv with b a constant and we assume that the particle continues to oscillate how does the period change?

## Homework Equations

F= m a ; v'= a; x'= v; x''= a[/B]

## The Attempt at a Solution

So my idea was creating the differential equation of the motion:

Before the external force to be applied :

m x" + k x= 0 (there, must be a force F=-kx even if the problem doesn't mention it so that the harmonic motion exists before the application of the external force) so T= 2 pi (m/k)^0.5[/B]

After the force:

mx'' + b x' + k x= 0 , the problem is that this equation has not as a solution a function like this x (t)= A cos ( wt + phi) but a linear combination of exponential function so I can't figure out what the period is... (to solve the equation is used wolfram alpha and it doesn't give me a sinusoidal function)

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