Whether or not the particle performs complete oscillations?

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SUMMARY

The discussion focuses on determining whether a particle attached to two elastic strings performs complete oscillations while undergoing Simple Harmonic Motion (SHM). The particle's equilibrium position is 2m from point A and 3m from point B. The condition for complete oscillations is established as u² < 3gk, where u is the initial speed, g is the acceleration due to gravity, and k is the spring constant. The participant clarifies the definition of "complete" oscillations, indicating a full cycle of motion without returning to the starting point.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Knowledge of elastic potential energy and spring constants
  • Familiarity with the concepts of equilibrium and oscillation
  • Basic physics principles including acceleration due to gravity (g)
NEXT STEPS
  • Study the mathematical derivation of SHM equations
  • Explore the relationship between spring constants and oscillation frequency
  • Investigate energy conservation in oscillatory systems
  • Learn about the effects of damping on oscillations
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of oscillatory systems and the principles of Simple Harmonic Motion.

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If you have a particle that is attached to two elastic strings moving with SHM. How can I determine whether or not the particle performs complete oscillations?

For example I have a particle that's at a point equidistant from A and B (which are the ends of the two strings), and say that the the point where the particle is at equilibrium is 2m from point A (and 3m from point B). If the particle is given a speed V when its at the midpoint of A and B towards the point of equilibrium, say it performs SHM with acceleration a=-(g/k)x. How can I determine using the information I have what I need for the particle to perform complete oscillations? Like, for example, if u^2<3gk then the particle will perform complete oscillations. (The values I used are examples and aren't correct.)
 
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What do you mean by "complete" oscillations?
 
Nevermind, I got it. :smile:
 

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