Oscillating compass needle – July 8 2024 – COMSOL FILE Version 6.2
The model above features an oscillating bar below a fixed bar. The bar oscillates due to an applied body force of 0.1N/m. This is slightly larger than the calculated k=0.067N/m. The reason for this disparity is the bar swings at a large enough angle for the amplitude to influence the force calculation. With small angles, the restoring force is approximately linear, however, restoring force = F = mg sin(Θ). Therefore at larger angles, the restoring force can no longer be approximated linearly and no longer follows sqrt(k/m).
Oscillation frequency = ω[rad/sec]
ω = sqrt(k/m)
ω=0.924 rad/s
J= 0.0785kg
k= ω2J
k= 0.067N/m
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html