Abstract: Normal modes and eigen frequencies are crucial characteristics of a multi-degree-of-freedom oscillation system. The influence of the coupling interactions between different degrees of freedom on the normal modes is a fundamental mechanical research topic，and is also relevant to various engineering and application problems. Here，we study the vibration of two identical leaf springs coupled with magnetic force. We show that the magnetic coupling causes a set of coupling-dependent modes，with the springs moving in opposite directions，and another set of coupling-independent modes，with the springs moving in same directions. In addition，the lower order vibration modes are more strongly affected by the magnetic force，while the higher order modes of the two springs are barely coupled. Thus，the two springs would have distinct vibration frequency spectrums if their initial conditions are different. We have also performed experiments，to observe the vibration phenomena and measure the eigen frequencies with different key variables，including the spacing distance of the springs，spring thickness and length. The experimental results are all in accordance with our theoretical predictions. 

Key words: mechanical oscillation, normal mode , magnetic interaction