Stiffness in mass spring system


by Smileyxx
Tags: mass, spring, stiffness
Smileyxx
Smileyxx is offline
#1
Nov16-12, 04:27 PM
P: 35
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.
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SHISHKABOB
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#2
Nov16-12, 04:30 PM
P: 615
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
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#3
Nov16-12, 04:34 PM
P: 35
Quote Quote by SHISHKABOB View Post
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?
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
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#4
Nov16-12, 04:44 PM
P: 615

Stiffness in mass spring system


[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
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#5
Nov16-12, 04:53 PM
P: 35
Quote Quote by SHISHKABOB View Post
[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?
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
SHISHKABOB is offline
#6
Nov16-12, 05:03 PM
P: 615
Quote Quote by Smileyxx View Post
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?
[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
Smileyxx is offline
#7
Nov16-12, 05:04 PM
P: 35
Quote Quote by SHISHKABOB View Post
[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]
Thanks alot


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