# non-linearly. ! As height ( H ) increases, ( f ) decreases, $ % - PowerPoint PPT Presentation

A Model for Resonance As stiffness ( k ) increases, the resonant frequency ( f ) increases, # non-linearly. ! ∝ As height ( H ) increases, ( f ) decreases, $ % & non-linearly. As mass ( M ) increases, ( f ) decreases, non-linearly.

So in terms of our testing of model buildings: The higher the frequency at which the earth shakes, the greater the energy intensity the earthquake produces and thus the greater the force the shaking ground exerts on the buildings. We can use the equation above to predict how much a certain Force will displace x (move away from vertical) a building if we know the stiffness k of that building. So, to minimize the displacement x of a building when it is shaken by an earthquake Force , the building should have as high a stiffness k as practical. x = Force/ k

SOLUTION Thus, the resonant frequency decreases to about 0.7 x of the original when the mass is doubled (2X).

Example 2. If you know the resonant frequency of one building f 1 , and you increase the height by 2x, what happens to its resonant frequency? Calculate it with this equation. 1 ! " = % ' ( )

SOLUTION

Resonance and Building Stiffness

SOLUTION

Example 4. If you know the resonant frequency of one building f 1 , and you increase its mass 3x and you reduce its height to half of its original, what happens to its resonant frequency? 1 ! " = % ' ( )

SOLUTION Example 4. If you know the resonant frequency of one building f 1 , and you increase its mass 3x and you reduce its height to half of its original, what happens to its resonant frequency?

Example 5. If you know the resonant frequency of one building f 1 , and you increased its resonant frequency to 10x its original f 1 by changing the building’s height, how much did you change its height? Calculate it with this equation. 1 " # = % ' ( )

SOLUTION Example 5. If you know the resonant frequency of one building f 1 , and you increased its resonant frequency to 10x its original f 1 by changing the building’s height, how much did you change its height? Calculate it with this equation.