Question

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

Answer 1

As here figure is missing so i m assuming the data here

Mass of plate = 1 KG , Dimension = 1m$\times$ 1m, speed of air = 10 m/s, and torsional stiffness= 10 Nm/rad,

$f_n=\frac{1}{2\pi}(\sqrt{\frac{CJ}{I_Al_A}}$

$f_n=\frac{1}{2\pi}(\sqrt{\frac{10\times bd^2 }{6\times mass\times l^3}}$

$f_n=.205$ $f_n=\frac{1}{2\pi}(\sqrt{\frac{10\times 1\times 1^2 }{6\times 1\times 1^3}}$

$f_n=0.646$ Hz

this is frequency of oscillator