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.