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

AI Thread Summary
A 5kg block in simple harmonic motion (SHM) is connected to a spring and initially displaced 15cm from equilibrium. The block reaches maximum displacement after 0.3 seconds, leading to the equations 15=A cos(ø) and 0.3ω+ø=0. The discussion highlights the challenge of solving for three unknowns with only two equations, suggesting that the spring constant (k) is necessary for a complete solution. One participant proposes using kinetic energy principles to derive the spring constant, indicating that this could facilitate solving the problem. The conversation emphasizes the need for additional information, specifically the value of the spring constant, to fully address the question.
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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\times
amplitude\div2=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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