Formula for Natural Frequency of Cantilever Beam

[Oscar6330]

I found two different versions of equations to find natural frequency of a cantilever beam. I am not sure which one is right. I would appreciate if someone could make things a bit clear here


F1= k^2*sqrt(E*I/(mpl*L^4))/(2*pi) where k=1.875 for first natural freq and I= b*d^3/12;

OR is it

F1= k^2*sqrt(E*I/(mpl*L^4)) where k=1.875 for first natural freq and I= b*d^3/12;

Basically I am not sure why some equations have /(2*pi) while others do not and which one is correct

 

[Studiot]

Angular frequency , $\omega$ radians /second = 2$\pi$f cycles per second ?

 

[Oscar6330]

Angular frequency , $\omega$ radians /second = 2$\pi$f cycles per second ?

Thanks. So the first equation gives freq in Hz while other one gives answer in radians per second?

 

[Studiot]

Yes the solution to the governing differential equation for say a cantilever with mass m at the end is

$$m\ddot x + kx = 0$$

which has solution

$$\omega = \sqrt {\frac{k}{m}}$$

where omega is in rads/second

 

[Oscar6330]

Yes the solution to the governing differential equation for say a cantilever with mass m at the end is

$$m\ddot x + kx = 0$$

which has solution

$$\omega = \sqrt {\frac{k}{m}}$$

where omega is in rads/second

thanks for your kind reply.

So

F1= k^2*sqrt(E*I/(mpl*L^4))/(2*pi)


w1=k^2*sqrt(E*I/(mpl*L^4))