Linearising Graph of Mass and Frequency

[Tikiboom1]

Homework Statement

I did an experiment about the loading of tuning forks. I added blue tac to one of the prongs on a tuning fork and then weighed it. I then measured the different frequencies for each mass and plotted a graph which ended up looking like a exponential decay graph. The results are shown below :

Mass(kg): Frequency(Hz):
0.05179 307.83
0.05219 305
0.05269 302.83
0.05335 301.17
0.05378 299.83
0.05572 299.17

Homework Equations

ω = 2πf
ω = √(k/m)

The Attempt at a Solution

When a tuning fork oscillates it is under SHM as when the prongs oscillate there is a restoring force towards the equilibrium. Using the equations of SHM, I did :
2πf = √(k/m)
∴ f = √(k/m) x 1/2π.

As, k and π are constants, we can rearrange the equation so that f = √k/2π x √1/m.
So if I plot f on the y-axis, and √1/m on the x-axis, I should get a straight line with √k/2π, being the gradient. However, I still get a exponential decay looking curve when I try to do that! I've then gone on to try the usual logging both sides and then plotting a graph of lg(frequency) and lg(mass) but I still get a curve which is extremely strange? I tried plotting frequency to (1/mass)². But still I get a curve? Could anybody please point out where I have gone wrong or done something careless? I can't seem to spot the problem and can't linearise the curve!

Thank you so much in advance, your help and advice is greatly appreciated!

 

[BvU]

Hello Tikiboom,

For your m you seem to take the mass of the entire fork. But not the entire fork vibrates ! So you want to work around your formula in such a way that you can plot your observation versus m. That way you can estimate m₀, the mass that doen's vibrate.

One other remark: why attach a weight to one prong only ? What frequency do you expect for the other prong ? How does that influence your measurement ?