Solving String SHM in Homework: Period & Speed

AI Thread Summary
The discussion revolves around solving a homework problem involving a particle attached to an elastic string undergoing simple harmonic motion (SHM). The first part of the problem requires calculating the period of SHM, which is determined to be 0.897 seconds, but some participants question its relevance due to the string becoming slack mid-motion. In the second part, the speed of the particle when the string becomes slack is calculated using both SHM equations and energy considerations, yielding different results, leading to confusion. Participants clarify the use of elastic potential energy and gravitational potential energy in their calculations, with some confusion about the modulus of elasticity and its application. The conversation highlights the complexities of applying SHM principles to elastic strings and the importance of understanding energy conservation in these scenarios.
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Homework Statement


A particle of mass 0.5kg is attached to one end of a light elastic string, natural length 1.2m, it has a modulus of elasticity of 29.4N. When at rest it lies 1.4m directly beneath A. The particle is then displaced 1.75m directly below A & released from rest.

Find the period of the simple harmonic motion which the particle moves with while the string is taut.
Calculate the speed of P at the first instant the string becomes slack.

Homework Equations


SHM equations?

The Attempt at a Solution



Okay well I'm having troubles understanding this question;

For the first half, I just plugged the numbers into the equation;

\omega^{2} mx = \frac{\lambda x}{l}

which, solving for T gives me 0.897s, the correct answer. What I fail to see is the relevance of this at all? This value for the time period is completely useless in this situation as it is no where near the time period for this particular system, where the string will become slack and fall freely under gravity for over half of the period...?

For the second half, similarly if I use the SHM equation for speed;

v^2 = \omega^{2} (A^2 - x^2) using A = 0.35m and x = 0.2m (above the eq'm position)

Solving for v I get 2.01m/s, again correct. However I then decided to use energy considerations;

Intuitively, the kinetic energy of the particle when the string becomes slack is the elastic potential energy lost minus the gravitational potential energy gained.

K.E = E.P.E - G.P.E

\frac{v^2}{4} = \frac{29.4*0.55^2}{1.2} - (0.5*9.8*0.55)

however this yields a completely different answer for velocity, namely 4.34m/s.

I can't see where I'm going wrong, I guess I've just got a problem imagining SHM being used for string in general, as I'm perfectly fine with spring related questions...

Thanks in advance
 
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Okay never mind about the second bit...I forgot it was / 2l =P.

BUT i would still love some clearance on the first bit.
 
Could please show what you did because I am getting 1.95m/s by the same energy considerations. Elastic P.E=3.705625 J and G.P.E=2.75 J.
 
The first bit is a tricky one. There is SHM only upto the point the string is taut so all talk of SHM would naturally end there. The particle's motion can not be described by SHM equations unless the string becomes taut again.
Another thing- moduli of elaticity is N/m^2. What is it doing there anyway?
 
aim1732 said:
Could please show what you did because I am getting 1.95m/s by the same energy considerations. Elastic P.E=3.705625 J and G.P.E=2.75 J.

You've got the GPE wrong 0.o no idea how..

I'm using the equation \frac{\lambda x}{l} as opposed to kx

So the unit of elasticity is N, and l is m. Are you thinking about youngs modulus?

And yeah, it's annoying because I'm confused as it is and it doesn't really help when the questions seem to be confusing me more in terms of their wording and what they're asking you to do :/
 
Sorry I was thinking about Young's modulus.
But you raise a point about G.P.E. If I am right there is no absolute measure of it. My datum is at the lowest point the mass goes so when the string becomes taut
GPE= m*g*h
=0.5*9.8*0.55 (A+s)
 
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