# Axial, torsional and pendulum modes of vibration(harmonic motion)

1. Sep 18, 2007

### intellegense

1. The problem statement, all variables and given/known data
Hello,

This is more of a conceptual question rather than a problem with numbers.
I was wondering if anyone new if there is a relationship between axial, tortional and pendulum vibration. The context is a mass hanging off a spring.

ie will the natural frequency of vibration be the same for all 3 types given the same mass and spring constant?

2. Relevant equations

3. The attempt at a solution

I tried an experiment and my apparatus is simply a mass hanging off the end of a spring. The only materials i had were an old school stop watch and a ruler so i had alot of difficulty getting any measurements. none fo which were any real use

i know that the natural frequency of axial vibration is

w(n)= sqrt(k/m)

where k= spring constant
m= mass
w(n)= natural frequency

i worked out the spring constant by graphing different masses versus deflection.

I also know the formula for frequency of a pendulum with a mass and a string, but not with a spring.

my common sense tells me that the natural frequency for all three modes of vibration will be the same when using the same spring and mass but i have no proof to back this up.

Ive searched the internet and havent found anything relevant.

Any hints would be great.