Displacement of Oscillating Block: y=A cos(ωt+ø)

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Homework Help Overview

The discussion revolves around a block in simple harmonic motion (SHM) connected to a spring. The original poster presents a scenario where the block's displacement and conditions at specific times are given, and they seek to derive the general equation for the displacement of the oscillating block.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to formulate equations based on the displacement at given times but expresses confusion over the number of unknowns relative to the equations available. They question whether additional information, such as the spring constant, is necessary to proceed.

Discussion Status

Some participants agree that the spring constant is a missing piece of information that complicates the problem. Others question whether the problem can be solved with the given conditions, indicating a lack of consensus on the sufficiency of the provided data. There are suggestions about using kinetic energy principles to derive the spring constant, but no definitive resolution has been reached.

Contextual Notes

Participants note that the problem may be lacking critical information, such as the spring constant, which is essential for solving the equations derived from the motion of the block.

paulzhen
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A block of 5kg connected to the free end of a spring is hanging from the ceiling and is in SHM. At t=0, the block is traveling upwards and its displacement is 15cm from the equilibrium. The block reaches its maximum displacement 0.3s later. What is the general equation of the displacement of the oscillating block_



y=A cos (ωt+ø)



I use t=0, y=15cm and t=0.3, y=A to get 2 equations:

15=A cosø
0.3ω+ø=0

However there are 3 unknowns in these 2 equations, and I just do not know how to get the 3rd equation from the given quantities. Is this question miss something? Should it tell me the value of force constant k or sth. else? Please help to solve, thanks a lot!

 
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They should have given the value of spring constant k.
 
lawmaker said:
They should have given the value of spring constant k.

really? is there no way to solve it with all known conditions?
 
Kinetic energy is 0 at the extremes in simple harmonic motion.So, Spring constant[itex]\times[/itex]
amplitude[itex]\div[/itex]2=0. This gives you the value of k(spring constant). Now you can solve the problem easily.
 
Last edited:
I am so sorry. It is spring constant times the square of the amplitude the whole divided by 2=0
 

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