Beams are basically rods supported at both ends or at one end.
Beams supported at both ends.
Let a beam be supported at both ends. If this beams is disturbed say from middle vibrations will be set up in it as shown in the figure.
The time period of the beam will be given by
T = \(2\pi\sqrt{\frac{Intertial \,factor}{Spring \, factor}}\)
Or T = \(2\pi\sqrt{\frac{m}{k}}\)
Since, Force F = mg
= kl
Where l is the depression in beam, we get
\(\frac{M}{k}=\frac{l}{g}\)
∴ T = \(2\pi\sqrt{\frac{m}{k}}\)
= \(2\pi\sqrt{\frac{l}{g}}\)
