I have to find an equation/model for the following:

A vibrating spring has damped harmonic motion- the oscillations decrease over time

-The centre of vibration is 0

-The starting amplitude of vibration is 0.6mm

-after 5 seconds the amplitude decreases to 0.5 mm

-During this time the spring moved forward and backwards 200 times

My attempt-

it will be a sine curve as centre of vibration is 0

The general form will be y=Ae^ax sin bx

200 forwards and backards= 100 cycles

if 100 cycles in 5 seconds then it is 100/5= 20 cycles per second = frequency (f)

T=1/f and T= 2pi/b and found b to be: 40pi

A=0.6? i.e. initial amount

It was 0.6 at 0s

0.5 at 5s

(0.5/0.6)=Ae^5x/Ae^0x

(A's cancel) therefore:

(0.5/0.6)=e^5x/e^0x

e^5x-0x=0.5/0.6

x= -0.036464

Can anyone tell me if I'm on the right track please , Im not sure if all of my working out is valid? if not could you please give the correct working out.

Thanks

Mathhelp246