Question

a square plate of L=1m side attached to a torsionnal spring of stiffness 10Nm/rad. The mass of the plate is M=1Kg. Now the air flow is coming from the left at 10m/s. What is the eigenfrequency (Hz) of the oscillator?

Answer 1

$\omega=2\pi\nu=\sqrt{\frac{k}{I}} \to \nu=\frac{1}{2\pi}\sqrt{\frac{k}{I}}$

$I=\frac{1}{12}m(L^2+L^2)=\frac{1}{12}\cdot 1\cdot(1^2+1^2)=1/6$ $kg\cdot m^2$

$\nu=\frac{1}{2\pi}\sqrt{\frac{k}{I}}=\frac{1}{2\cdot3.14}\sqrt{\frac{10}{1/6}}=1.23Hz$