# EMF induced in solenoid calculation

So, I performed an experiment where a bar magnet was allowed to drop through a solenoid connected to a voltmeter.

I have a graph of the voltage vs. time, and I have been asked to explain quantitatively the absolute value of the ratio of the maximum voltage to the minimum voltage. I have no idea how to do this.

We measured the length of the solenoid to be $0.11 \pm 0.005$ m and diameter was $0.03 \pm 0.005$ m, and the solenoid contained approximately $\text N = 3000$ turns. We also have the length of the bar magnet as $0.15 \pm 0.005$ m.

I suspect Faraday's law will be involved in the calculations, as will gravity, but I'm not sure how to get there. I could calculate $\vec{A}$ which is constant because I have the dimensions of the solenoid, but I don't know the strength of the field, and I don't have a function for the graph.

How can I proceed?

The lenz's rule states that the emf induced is $-N*\frac{d\phi}{dt}$ So, the change in magnetic flux with time is proportional to velocity. Thus, as the magnet goes through the solenoid, the voltage will go from a zero to a negative value and then increase as it comes out. The positive Maxima will be higher than the lower minima of the voltage vs time graph since the magnet is accelerating die to gravity. This the ratio required will be negative and just lesser than -1. Exact calculation will be difficult, since the modeling will require many assumptions. So, I guess that you use an oscilloscope with the appropriate settings and try. It can only be calculated experimentally.
P.S : The graph will look like the graph of $-sin(\theta)$ with the positive right part having a higher voltage.