# Max dynamic factor for sinusoidal load

• dwspacetime

#### dwspacetime

i posted it in general physics and got not answer. maybe this is the right place for this. thanks

here is a question for max dynamic factor for sinusoidal load F*sin(at). say the natural frequency is b for a mass. then the max DLF considering damping is

DLF=1/(1-(a/b)^2)

when a>>b DLF=0

what does that mean in the reality. it means if you apply a dynamic load with very very high frequency to a mass. the mass don't get any force? how come? why? thanks a lot.

DLF=1/(1-(a/b)^2)

when a>>b DLF=0
QUOTE]

This means only that the load changes its direction so often that it doesn't affect the natural motion observably.

What it says is that when you affect a mass through a spring and a dampener that have their position forced to oscillates between plus and minus some amplitude the mass will have a steady-state position response that is a similar oscillation about some position with a certain response amplitude. The ratio of the response amplitude relative to the driving amplitude will in general be a function of the driving frequency (and the natural frequency of the mass-spring-dampener which we assume is constant), and as you increase the driving frequency this ratio will go towards zero.

It is not correct to say that the mass do not get any force for high driving frequencies, it does. What you can say, is that the force the spring and dampener affects the mass with in this case oscillates so fast that the mass do not "have time" to move very much due to its inertia before the force has reversed direction.

It may help you to understand what happens if you think (or read) about the frequency response of the periodic driven dampened harmonic oscillator.

say a mass hung from ceiling from a spring and the ceiling remain still. we apply a dynamic force F*sin(at) to the mass. what will happen then.

if the mass does not move, and the resistance of the spring is proportion to its strain. if the spring does not change the length then there is not extra force applied to the spring which means the mass does not get any force. am i right

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No, the mass do get the force, but you have to include the effect of inertia of the mass which is the primary reason the amplitude of the mass position will go toward zero when the driving frequency goes to infinity. Since the force changes so fast it simply does not have time to do any significant work on the mass.

If you still have trouble picturing why this is so, consider applying the force F*sin(wt) to the mass m, but leave all other forces out. If you integrate the force up using Newtons law you will find that the position amplitude of the mass will be F/(m*w2) that is, as w becomes large the amplitude goes towards zero "at the square of the frequency" so to speak.

then how to get the force in the spring? i always think since it is linear so the max force in the spring shall be DLF*F. in the case that will be zero. am i right? thanks

I'm not really sure what you are asking about. The force of any (linear) spring is proportional with its deflection from its unloaded position. If the spring is attached to a wall at one end and a mass that almost doesn't move in the other, then the spring force will not vary much. In your case with gravity thrown in, the force will not be zero though, but oscillate closely around the force of gravity.

i am talking about the dynamic load the spring gets. if before and after we apply the dynamic load to the mass the spring length doesn't change then it does not get any more load other then the original gravity load from the mass.

i am talking about the dynamic load the spring gets. if before and after we apply the dynamic load to the mass the spring length doesn't change then it does not get any more load other then the original gravity load from the mass.

Yes, that is correct.

OK finally. then the mass didnt get any dynamic force either. how come

I'm not sure I can explain it any differently. Are you feeling I am explaining something you are not asking or do you disagree with my explanations?

Perhaps you can consider the driving force on a structure, like your mass and spring, to be replaced by a slowly varying force that on average would do the same work on the structure as the driving force do. With slowly I mean that the time scale is large enough to cover the transient response of the structure. For driving frequencies that are fast on this time scale the average work on the mass by the driving force is zero which then corresponds to an average force that is zero. This average force can be considered equivalent to the dynamical load.

interesting. if i am very angry and i grab your neck and yank you back and forth in a very fast way like the spiderman you are not going to get anything.

or i will break your neck?

or if i hold a sword and swing it horizotally in a very very high frequency. you think you can step in and try your neck or not? hahaha

those are serious questions.