Okay, so I've been trying to figure out what would be the time period of(adsbygoogle = window.adsbygoogle || []).push({}); spring of mass 'M'& spring constant K which is hung vertically from a ceiling.

Dividing the spring into n equal massless springs of spring constant k=nK which are connected to each other by n small objects of mass m=M/n like this-

_____Now, extension in first spring

n | (k)

m

:

:

3 | (k)

m

2 | (k)

m

1 | (k)

m

Δx1=mg/k

Similarly,

Δx2=2mg/k

...

Δxn=n mg/k

ΔX(Total)=ƩΔx=mg n(n+1)/2k

Putting values of m and k

ΔX=Mg n(n+1)/2Kn^2

Taking the limit n→∞

ΔX=Mg/2K which corresponds to an effective mass of M/2 rather than M/3 as given in Wikipedia & other websites.

I would be grateful if someone would be able to explain what i am doing wrong.

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# Effective Mass of Spring

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