Solving the Oscillation of Mass-Spring System

[bon]

Homework Statement

Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2

What is the fractional change in amplitude of oscillation in one complete oscillation?

Homework Equations

The Attempt at a Solution

Ok so I've written down the DE:

x'' + Bx' - Ax = 0 and solved..but this gives be Ce^-Lt + De^-L't where C, D, L and L' are constants...

1) i don't see how this oscillates... 2) how do i work out fractional change in amplitude of oscillation?

 

[tiny-tim]

Hi bon!

(try using the X² tag just above the Reply box )

Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2
…
x'' + Bx' - Ax = 0

Nooo

 

[bon]

Why not? I thought this was a direct consequence on NII (and cancelling the m)

 

[tiny-tim]

One of the signs is wrong.

 

[bon]

ok i see thanks i can now solve the eqn but how do i find fractional change in amplitude of oscillation

 

[tiny-tim]

Well, what's your solution now?

 

[bon]

not to worry - i get it now. thanks