Forced Oscillations of Mass-Spring System: Reasons for Observed Behaviour

[nokia8650]

A mass spring system with natural frequency of 1.5Hz is set up as shown:

http://img300.imageshack.us/img300/7922/35809066dx2.th.jpg

Can someone please explain the reasons for the following observations:

When the support rod oscillates at a frequency of 0.2 Hz - oscillations are (almost) in phase with driver

When the support rod oscillates at a frequency of 1.5 Hz - oscillations have a phase difference is pi/2 radians with the driver.

When the support rod oscillates at a frequency of 10 Hz - oscillations are out of phase with driver [or phase lag of (almost) pi on driver]

Thanks

 

[Carid]

Here's a good resource

http://www.walter-fendt.de/ph14e/resonance.htm

Check out the phase difference diagram

 

[thomate1]

for your question. The observed behavior of the mass-spring system can be explained by the principles of forced oscillations and resonance. When the support rod oscillates at a frequency of 0.2 Hz, it is close to the natural frequency of the system (1.5 Hz). This means that the system is able to easily absorb the energy from the driver and oscillate in phase with it. This is known as resonance, where the amplitude of the oscillations is at its maximum.

At a frequency of 1.5 Hz, the system is oscillating at its natural frequency. This means that it is able to absorb energy from the driver and oscillate with a maximum amplitude. However, since the driver is also oscillating at the same frequency, the two oscillations are out of phase by pi/2 radians. This is because at the natural frequency, the system is at its maximum displacement while the driver is at its equilibrium position. This phase difference is a result of the energy exchange between the system and the driver.

When the support rod oscillates at a frequency of 10 Hz, it is far from the natural frequency of the system. This means that the system is not able to efficiently absorb energy from the driver and as a result, the amplitude of the oscillations is lower. Additionally, the system is out of phase with the driver, with a phase lag of almost pi radians. This is because the system is not able to keep up with the rapid oscillations of the driver at this frequency.

In summary, the observed behavior of the mass-spring system can be attributed to the principles of forced oscillations and resonance. The natural frequency of the system plays a crucial role in determining the amplitude and phase of the oscillations when driven by an external force. I hope this explanation helps to clarify the reasons for the observed behavior.