# Well Winching Conundrum

Consider a well which has a swinging bucket of nugatory size dangling from a massless rope- forming a simple pendulum. The rope's initial length is 20 metres, but I begin to winch the rope upwards at a regular rate to a length of 2 metres, which takes one minute. During this time, how many full swings (or oscillations, assuming I start winching when the bucket is at a point of equilibrium) does the bucket complete?

Ignore friction/air resistance, and assume $$g=9.8 \text{ ms}^{-2}$$.

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