Oscillations of a weighted ruler

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SUMMARY

The discussion centers on the oscillation of a weighted ruler, specifically how the removal of weights affects its period and amplitude. The formula for angular frequency, w = √(k/m), indicates that a decrease in mass (m) results in a decrease in angular frequency (w), subsequently increasing the period (t) of oscillation. The amplitude, defined by the maximum displacement in simple harmonic motion, increases when the weights fall off, as the maximum displacement becomes greater without the added mass.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the equations of motion, specifically w = √(k/m)
  • Knowledge of angular frequency and its relationship to period
  • Basic grasp of oscillatory systems and their dynamics
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  • Study the equations governing simple harmonic motion in detail
  • Explore the effects of mass changes on oscillatory systems
  • Investigate the relationship between amplitude and maximum displacement in oscillations
  • Learn about the physical principles behind oscillations in mechanical systems
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Students of physics, educators teaching mechanics, and anyone interested in the dynamics of oscillatory systems will benefit from this discussion.

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Hi everyone. Can you imagine a metre rule attached to a tabletop and weights are attached at the other end? The ruler will sag. The ruler is then given a push to let it oscillate. However the weights fell off when it is oscillating. So what is the effect on period and amplitude?

I did:

Since w=sqrt of k/m, when m decreases w decreases.
w=2pi/t, thus t will increase.

However, although i cannot think of any equation that affects the amplitude (I think it is constant), but my answer script says that amplitude actually increased. Can anyone use equations to prove that to me?

Thank you!
 
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The equation that affects the amplitude is the equation of simple harmonic motion. This equation states that the amplitude of the oscillation is equal to the maximum displacement of the particle. Since the weights had fallen off, the maximum displacement will increase leading to an increase in the amplitude.
 

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