Determine The Natural Frequency

[cxz7410]

Determine the natural frequency in Hz of the system sketched below given the following values:

Mass m=4kg Spring stiffness k=28kN/m Length a=121mm Length b=93mm

 

I know that
ω=(k/m)^0.5
so probably I need to find m
should I write m=4*9.81*(0.93+1.21)?

[OceanBreeze]

From electrical theory,  the resonant frequency = 1/2π√LC

 

The mechanical equivalent is 1/2π√k/Meff

 

You need to first find the effective mass of the system. I don’t think your approach at that is right.

 

The effective mass can be quite complicated and you may need to use a Lagrangian.

I am not entirely sure of the correct method but if I have the time I may look into it as I enjoy these types of problems. You might have a look here for some inspiration, particularly the last part on the inverted pendulum with an oscillatory base.

 

Out of curiosity, is this an academic exercise or a practical exercise? In other words, does that design have some practical application as perhaps in seismology?