Register to reply

Effective Mass of Spring

by ShakyAsh
Tags: effective, mass, spring
Share this thread:
Nov17-12, 06:03 AM
P: 6
Okay, so I've been trying to figure out what would be the time period of 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-
n | (k)
3 | (k)
2 | (k)
1 | (k)
Now, extension in first spring
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.
Phys.Org News Partner Physics news on
Symphony of nanoplasmonic and optical resonators produces laser-like light emission
Do we live in a 2-D hologram? New Fermilab experiment will test the nature of the universe
Duality principle is 'safe and sound': Researchers clear up apparent violation of wave-particle duality
Philip Wood
Nov17-12, 10:49 AM
PF Gold
P: 953
I think what you are doing wrong is to assume that the effective mass of the spring for static extension (equilibrium) is also the effective mass for the dynamic case (oscillations).

The oscillations of a spring with distributed mass will be in the form of standing (stationary) waves. The case you are probably interested in is the fundamental mode. The mathematics is more complicated than for a lumped mass on a massless spring.

Register to reply

Related Discussions
Effective mass of spring Classical Physics 0
Spring mass spring mass spring - 2 balls oscillations General Math 1
Effective masses of spring-mass systems Introductory Physics Homework 6
Effective Spring Constant Introductory Physics Homework 0