You are Here: Home >< Physics

# Proving expontential decay graphs watch

1. I did an experiment measuring the amplitude of swing of an object in simple harmonic motion with time. I have drawn a graph of amplitude against time, but I need to prove this is an exponential decay graph. Are there two variables i could plot that should give a straight line graph if my experiment follows the expontial decay law?
The half lifes from my first graph aren't very good, so i need a graph that doesn't rely on me attempting to draw a curve.
Thanks.
2. If amplitude is experiencing exponential decay with respect to time then the equation of the line will be...

A = (A.MAX) x (e^ -(k x t))

Therefore...

k = -(ln(A/A.MAX))/t

to show that its exponential decay, k must be approx. constant.

use about 5 - 10 values of A & time and see if k is roughly the same.

EDIT: A = Amplitude at time, t
A.MAX = Maximum amplitude of motion
t = time

Or if your intent on using a graph...

A = (A.MAX) x (e^ -(k x t))
ln A = - kt + ln(A.MAX)

look familiar...?

y = mx + c [y=lnA, m=-k, x=t & c=ln(A.MAX)]

So you'll have to plot values of time against lnA at that time. If the resultant curve shape is straight, you've got yourself an exponential decay relationship between A & t.

Hope that makes some sense.
3. plot a graph of ln A against no. of swings. (ln = natural log)

for an exponential decay this will be a straight like with a negative gradient equal to -K where K is the decay constant

the "half life" of the decay should also be constant and equal to ln 2 / K
4. ok, that makes sense.
Thanks so much for your help!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 12, 2007
Today on TSR

### University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University