Determine the natural frequency

[cxz7410]

Homework Statement

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

Homework Equations

ω=(k/m)^0.5

The Attempt at a Solution

so probably I need to find m
should I multiply 4*9.81*(0.93+1.21)?

 

[mfb]

ω=(k/m)^0.5

m is used for the mass already, you shouldn't reuse symbols for different things. Where can you use that formula?

What is the potential energy of the system (and its components) if the spring is extended by a length x?

 

[haruspex]

ω=(k/m)^0.5

That formula only applies to the usual simple arrangement of spring and mass.

probably I need to find m

While it is true that you can make your quoted formula work by finding an "effective" mass for the m in it to represent, it is not at all obvious how to find it. Indeed, that approach would be backwards. You need to find the equation of motion from first principles. Having found that you will see what the effective mass is in this arrangement. It is a very bad idea to go making wild guesses.