Solving Simple Harmonic Motion Question

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SUMMARY

The discussion centers on the implications of applying an initial velocity U to a particle in Simple Harmonic Motion (SHM) at maximum displacement. It concludes that the equations of motion can still be used, but the reference point for displacement must be adjusted. The participant must decide whether to treat the scenario as a continuation of the original SHM or as a new SHM with a different initial condition. The integration process for deriving the equation of motion, specifically x = a sin(ωt), can become complex depending on the chosen initial conditions.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM) principles
  • Familiarity with the equations of motion in SHM
  • Knowledge of integration techniques in physics
  • Concept of maximum displacement and velocity in SHM
NEXT STEPS
  • Study the derivation of equations of motion for SHM with varying initial conditions
  • Explore the impact of initial velocity on the characteristics of SHM
  • Learn about the mathematical techniques for solving complex integrals in physics
  • Investigate the concept of phase shifts in SHM and their implications
USEFUL FOR

Physics students, educators, and anyone interested in advanced concepts of Simple Harmonic Motion and its mathematical modeling.

acmmanoj
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I am having a question and tries to solve a problem for days. Consider general SHM. When the particle reaches to the maximum displacement, a if a velocity U is given to the particle towards to the center of SHM, (keeping the same force mω^2x)

1. What would happen to the SHM...is it same or can i use same equations or should i derive equation again

Should i consider this as new SHM ( X=a when t=0) or should i continue from same SHM (X=0 when T=0)

2. if i derive again, which point should i considered as center, what will happen to the displacement and maximum displacement...is it same or difference

3. when tries to get equation of motion as x=asin(ωt) from intergartion it produces a very complex equation. (in intergration i took, when x=a , v=u and x=a t=0)
 
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