The discussion focuses on designing a cantilever beam to achieve a specific resonant frequency using the equation w = sqrt(k/m). Participants clarify that the angular frequency (w) must be calculated in radians per second by multiplying the frequency in Hertz (f) by 2π. The mass (m) of the beam is determined by its density multiplied by its volume, while the stiffness (k) is specific to the beam's material and geometry.
PREREQUISITESMechanical engineers, structural engineers, and students studying vibration analysis and beam design will benefit from this discussion.
No.engineer23 said:Homework Statement
The problem is to design a cantilever beam with a certain resonant frequency.
Homework Equations
w = sqrt (k/m)
The Attempt at a Solution
I know k for a beam and m can be written as density * volume.
My question deals with the w. If I am given a frequency in Hz, can I plug it in for omega directly?
Yes. The angular frequency w, in radians/sec , is the natural frequency, f , in Hz, multiplied by 2*pi. The equation you note is for the angular frequency.Or do I need to multiply by 2*pi first?