natural frequency system mass spring

[Cholito]

Good morning to all, I am experiencing a problem with this exercise. I am asked to obtain the natural frequency of the mass system springs on the sloped plane as shown in figure. I think it doesn't depend on alpha but beta somehow yes.
thanks for the help and good day.

 

[Stan9411]

if the k spring stretches as much as the m mass moves, the proper frequency of the system is the classic sqrt(k/m)

the slope of the slide defines you only the static balance of the system that will be a stuff like:

xst = mgsin(beta)/k

but if you write the answer to a harmonic force f at frequency w, you will see that the system goes in resonance simply if w = sqrt(k/m)

p.s: on this forum when an idea arises, before asking for confirmations or opinions.

 

[Cholito]

thank you very much, very kind