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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Effective Mass of Spring

**Physics Forums | Science Articles, Homework Help, Discussion**