Forced oscillations vs Natural frequency

[Victorian91]

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..

 

[nasu]

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?

 

[JolileChat]

I guess he tried to express the excitation as: F=cos(w*t-pi/2)

 

[Victorian91]

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..

 

[sardar]

Forced oscillations and natural frequency are two important concepts in the study of oscillatory systems. Forced oscillations refer to the motion of a system that is being driven by an external force, while natural frequency is the frequency at which a system will oscillate when undisturbed.

When the frequency of the forced oscillation is Pi / 2 radians out of phase with the natural frequency of the system, it means that the two frequencies are perpendicular to each other. In this case, the amplitude of the spring mass system will indeed reach a maximum, as the external force is acting in a direction that is perpendicular to the natural motion of the system. This is known as resonance.

Resonance occurs when the frequency of the external force matches the natural frequency of the system, or is a multiple of the natural frequency. In this scenario, the amplitude of the oscillations will continue to increase, potentially leading to the failure of the system if the force is too strong.

In summary, you are correct in your understanding that when the frequency of the forced oscillation is Pi / 2 radians out of phase with the natural frequency, the amplitude of the spring mass system will oscillate at a maximum amplitude due to resonance. However, it is important to note that this situation can be potentially dangerous for the system and precautions should be taken to prevent excessive amplitudes.