Stiffness in mass spring system

Smileyxx

1. The problem statement, all variables and given/known data
What happens to the frequency of oscillation if stiffness increases and why?


2. Relevant equations

?

3. The attempt at a solution
Frequency increases but trying to figure out why.

SHISHKABOB

By stiffness I'm assuming you mean the spring constant, often known as k. It's found in Hooke's law F = -kx where F is the force the spring is exerting and x is the distance from the equilibrium point.

Don't you have some equations relating the frequency of the oscillations of the spring-mass system and the spring constant of the spring?

Smileyxx

a=[2pie f]^2x. So if k increases f increases which increases a(acceleration) and according to the formula given at the start frequency increases. If that make sense

SHISHKABOB

[itex]a = \left( 2 \pi f\right)^{2x}[/itex] ?

I don't recognize that equation >.> I'm very sorry

do you recognize

[itex]x \left( t \right) = Acos \left( \omega t - \phi \right)[/itex]

where

[itex]\omega = \sqrt{ \frac{k}{m}}[/itex]

is the angular frequency of the oscillation, A is the amplitude and [itex]\phi[/itex] is the phase shift?

Smileyxx

Its a = \left( 2 \pi f\right)^{2} x.
I dint knew the 2nd equation but i get it now. stiffness is proportional to frequency according to that.but does the natural frequency of spring increases as well?

SHISHKABOB

[itex]a = \left( 2 \pi f\right)^{2}x[/itex] makes much more sense :)

angular frequency is just the natural frequency times 2π

or

[itex] \omega = 2 \pi f[/itex]

Smileyxx

Thanks alot