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Question in SHM lab! please help!

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i have a design lab to do and state what is the relation between length of spring and time period of a spring oscillation. however i tried to plot ln(time period) y and ln(length) x but i dont know what to do next. i dont know what the gradient that i will find will stand for.... Please help... maybe of you can tell what should the outcome of my calculations or something that would help me find an equation with time period and length of spring...

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If the mass of the spring is negligible compared with that of the load that it supports, the period of the oscillation should be independent of the length of the spring! (It only depends on the mass of the load and the spring constant).

This contrasts with the case of a pendulum, for which the period of oscillation depends on the length but is independent of the mass.

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i just got disappointed HAHA. yes this may be the case!!! seems legit. so i just use hookes law right????

If Hooke's law applies to the spring (i.e., it is not overstretched), the period of the oscillation with mass m and spring constant k should be T = 2pi * sqrt(m/k)

actuall with the dat i got time period and length what do you suggest me to do???

You could see whether the period is independent of the length, as predicted by the simple theory.

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the thing is that there is a perfectly linear relation to their logs and a quadratic or cubic relation as far as as the trend is concerned... i dont now how to put if you see what i mean

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Did you alter the length of the spring by clamping it at different points, or did you use a set of springs that might have different spring constants? Was the amplitude of the oscillation small enough for it to remain SHM?

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Did you check that all the springs had the same spring constant? And were the masses of the springs negligible compared with the mass of the load? If not, the effective mass would have been different for each spring.

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If you're sure about the spring constants you could calculate the total effective masses from the different periods. Subtract the mass of the load to get the effective mass of the spring in each case.

That makes your experiment quite an interesting one.

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ok thank you very much for your help and i appreciate it!!!!!!!! :D but the problem is that i dont know the exact value of the spring constant... i have only the mass used, the data period and the length... as it seems it cant be worked out... thank you anyway!!!!!!!!!!!

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