- #1

Auror

- 4

- 0

restoring force,##\vec F_r=-kx\hat{x}##

and damping force,##\vec F_d=-bv\hat{v}##

When the oscillating object goes towards amplitude position from equilibrium position,direction of velocity and position(##\displaystyle \vec x##) is same. For that , net force,##\vec F=\vec F_r+\vec F_d## can be written as(just putting values)- ##F=m\ddot x=-kx-bv...(1)##.

But when the oscillating object moves back from that amplitude position to equilibrium position,direction of velocity changes,but direction of position doesn't. So direction of damping force changes. Hence direction of restoring force and direction of damping force are opposite. So net force should be, ##F=m\ddot x=-kx+bv...(2)##

While solving differential equation for damping- we used (1) only which gave the differential equation,

##m\ddot x+kx+b\dot x=0##

But what about the equation 2 which we didn't deduce but is valid simultaneously? Why doesn't change of direction of damping force count here?