Forced oscillations vs Natural frequency

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When the frequency of forced oscillation is Pi/2 radians out of phase with the natural frequency of a spring-mass system, it can lead to maximum amplitude oscillations. The discussion clarifies that frequency itself is a numerical value and does not inherently possess phase, unless considering complex frequencies that account for dissipation. A graph plotting phase difference against frequency indicates that at the natural frequency, the phase difference is indeed Pi/2 radians. It is noted that maximum amplitude occurs when the driving and driven pendulums are in phase. Overall, the relationship between phase difference and amplitude in oscillatory systems is emphasized.
Victorian91
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What happens if the frequency of the forced oscillation is Pi / 2 radians out of phase of the natural frequency of the spring mass system? I guess this makes the amplitude of the spring mass system to oscillate at a maximum amplitude.. Am I correct? Thanks in advanced..
 
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Victorian91 said:
What happens if the frequency of the forced oscillation is Pi / 2 radians out of phase of the natural frequency of the spring mass system? I guess this makes the amplitude of the spring mass system to oscillate at a maximum amplitude.. Am I correct? Thanks in advanced..

How can the frequencies be "out of phase"? Or in phase.
Frequency is a number, a quantity. It has no phase. Unless you mean some complex frequency, that includes dissipation.
Can you explain more?
 
I guess he tried to express the excitation as: F=cos(w*t-pi/2)
 
First of all I would like to apologize if I made myself unclear..

Anyway here it goes..
Basically, if we plot a graph of phase difference between the driving pendulum and driven pendulum against the frequency of the forced oscillation, at the natural frequency of the pendulum, the phase difference will be Pi / 2 radians. Is this correct?

I thought that if the driving pendulum and the driven pendulum is in phase it will have maximum amplitude..

I hope that my description now clears the air more.. Thanks alot..
 
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