Is there a func' for ideal x-section area in a resonant beam?

[silverslith]

Obviously it has to taper from the fixed end to the most mobile one. Or from the centre (node) of a symmetrical one to the ends (antinodes).

Talking about longatudinal harmonic resonance only here.

Ideally the static instants at full compression or tension would give a constant percentage length change from unloaded along the rod.

Does it follow that at any giventime, a point X distance from the node, has Velocity and acceleration: both proportional to X or am I confused?

I'm pretty sure this is an integration of shm mass/spring systems or somesuch.

Is there a formula that emerges for the rate of taper of the crossectional area for a given material elastic modulus and frequency?

 

[Almsco]

Yes, there is a formula that can be used to calculate the rate of taper of the cross-sectional area based on the given material elastic modulus and frequency. The formula is F = k/x, where F is the frequency, k is the spring constant, and x is the distance from the node. This formula can be used to calculate the rate of taper of the cross-sectional area.