Simple harmonic motion + rate of changes

AI Thread Summary
The discussion focuses on a physics problem involving a 2.0 kg bucket with 10 kg of water suspended on a spring with a constant of 125 N/m, oscillating with a 3.0 cm amplitude. A leak develops, causing water to flow out at a rate of 2.0 grams/s, prompting questions about the period of oscillation and how it changes over time when the bucket is half full. Participants are encouraged to demonstrate their understanding of the relevant equations for mass-spring systems. Additionally, there are comments on the proper use of language regarding the terms "hung" and "hanged" in context. The conversation emphasizes clarity in problem-solving and communication.
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A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm.
Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket is half full:

a) determine the period of oscillation and the rate at which the period varies with time.
b) What is the shortest period that this system can have?
 
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Welcome to PF:
To get the best out of this forum, please show us how you have attempted the problem yourself. Do you, for instance, know the equation for the period of a mass on a spring?Your English is pretty good! Just a few tips...

the bucket is "hung" not "hanged" ... "hanged" means you've killed it via a popular execution method and is usually reserved for humans. "hung" is fine for inanimate objects and lumps of meat, thus: "The man was hanged, then he hung there."

"the bucket springs a leak" or "the bucket starts leaking" ... this is a tricky one since it relied on idiom. It is reasonable to say "the bucket becomes leaky" or "a leak arises in the bottom" but pretty unusual.
 

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