Physics coursework help needed!

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Am doing a2 Physics coursework on damped oscillations

Here is my introduction, but i have no idea what to do on background theory can anyone help?

In my experiment I will be investigating the exponential decrease in the amplitude of oscillations using a simple laboratory arrangement. I will vary the air resistance on the mass, using different size cards. I will also vary the time to see what affect these have on the amplitude of the oscillation. I will keep the mass constant while changing the sizes of the card, and measuring the amplitude of the oscillation for different times. The mass will be 20g and the amplitude of the oscillation will be measured using a ruler. I will do this for five different size cards in increments of 1cm², starting with a card of 2 cm² and finishing at 7cm² and six different times starting at 5 oscillations and finishing at 30 oscillations. When I have sufficient results I will plot graphs of amplitude against time, which will show the characteristic exponential decrease. Then I will find the ‘half-life’ of the graphs by determining the time it takes to decrease to half its initial value. By changing the size of the graph it is possible for me to change the degree of damping and hence alter the half-life.
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