This active web form can be used to calculate the first 2 modes of a general beam configuration.  Up to 24
different beam segments can be used with each having different section and area properties including weight
density.  Concentrated weights can also be added.  Boundaries include free, simple support and fixed slope.  
Both vertical and rotational springs can also be used.

Output includes the first 2 mode frequencies in Hz and the respective mode shapes.  A gravitational constant
must be defined.  All dimensional units must be consistent with each other and Hz.

L is the length of each segment, E the elastic modulus, I the area moment of Inertia, A and ρ the cross
sectional area and weight density, W concentrated weight the , ∆ and θ deflections and rotations, ky and kθ
vertical and rotation springs.  Any consistent set of dimensional units can be used.  Angles are in radians.

Change or add values to any of the white cells and the frequencies are automatically updated.
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