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Damped SHM

Hey guys, was hoping you could answer a few questions I have about damped SHM.

Right, so assume I did an experiment where I set a pendulum going and tried to measure the decay of amplitude basically.

I set a timer going and I measured the peak amplitude after each oscillation and used the corresponding time to create a table of values. I then took the log of the amplitudes and graphed lnA against the time that had passed. I get a straight line which has a negative gradient.

As I understand, had I started with a greater amplitude: the y-intercept would increase but the gradient would stay the same, as the rate of decay would still be the same.

Had I attached some card with large surface area onto the pendulum: the gradient would be steeper, because the rate of decay would increase. Y-intercept would remain the same.

My question is: How would changing the length of the string affect my graph? I know that increasing the length would increase the time period. However, am I correct in thinking that the graph would not be affected, because the air resistance that the pendulum has to overcome during each oscillation is the same? Or is there more to it?

TLDR: How does changing the length of the string on a pendulum affect the rate of decay of amplitude?

Thanks guys!
Reply 1
Avatar for Joinedup
Joinedup
20
I think here you'd want to look at the speed attained by the bob and the air resistance (stokes)
Reply 2
Avatar for Hamburglar
Hamburglar
OP
Original post by Joinedup
I think here you'd want to look at the speed attained by the bob and the air resistance (stokes)


I've been thinking about it for a while now. Maybe with a decreased time period, the frequency increases and so since the speed is greater, it cuts through more air per second and so the damping force is greater?

Thanks for the response

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