Simple harmonic motion in a string

AI Thread Summary
The discussion revolves around a problem involving a light elastic string with a particle attached, requiring the calculation of the time it takes for the particle to return to its original position after being released. The equations of motion are established, with tension calculated as T = 40x and acceleration as a = -100x. It is clarified that, unlike a spring, the string cannot resist compression, leading to a different motion pattern. The particle takes a quarter cycle to return to the string's natural length, then moves unimpeded to point O and beyond. The key takeaway is understanding the unique behavior of the string in simple harmonic motion.
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Homework Statement


Hi
I need some clarification on this question
A light elastic string of natural length 50 cm and modulus 20 N has one end fastened to O on a smooth horizontal table. The other end has a particle of mass 0.4 kg attached to it and the particle is released from rest at a distance 60 cm from O. Find the time it takes to reach O.


Homework Equations





The Attempt at a Solution


While the string is stretched
T=kx/l
=20x/0.5
=40x
40x=-.4a
So,a = -100x

w=10
T=2pi/10 =pi/5

I get stuck from here. Can anyone help please? Thanks
 
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Think about how the mass moves after it's released. If the string were a spring, the mass would take a quarter of a cycle to return to its natural length, another 1/4 cycle to get to its farthest point, and 1/2 cycle to come back.

However, this is a string, which means it can't resist any compression. The mass would take 1/4 cycle for the string to return to its natural length. After that, the mass moves unimpeded all the way to O and beyond.
 
Thanks a lot guys! Sorry for late reply.
 

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