Calculating Velocity in Simple Harmonic Motion: A Pendulum Clock Analogy

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SUMMARY

The discussion focuses on calculating the velocity of a particle executing simple harmonic motion (SHM), specifically using a pendulum clock analogy. It establishes that when the speed of the particle is half of its maximum speed, the displacement can be determined by analyzing the conservation of energy principles. At maximum displacement, the velocity is zero, while at the vertical position, the particle achieves maximum kinetic energy and velocity. The key conclusion is that the displacement corresponding to half the maximum speed occurs at a specific point in the motion, which can be derived from energy considerations.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Knowledge of kinetic and potential energy concepts
  • Familiarity with pendulum mechanics
  • Ability to apply conservation of energy principles
NEXT STEPS
  • Study the equations of motion for Simple Harmonic Motion
  • Learn about energy conservation in mechanical systems
  • Explore the mathematical derivation of velocity in SHM
  • Investigate the effects of amplitude on pendulum motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to explain the principles of simple harmonic motion through practical analogies.

jatin1990
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Homework Statement



Speed of particle executing simple harmonic motion with amplitude A is half of the maximum speed. At that instant, displacement of the particle is ?

Homework Equations





The Attempt at a Solution

 
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You have worded this question somewhat strangely but I will attempt a solution. Think of the particle under SHM as a Pendulum clock (or weight on the end of a string). If it is "ticking" then ask "what is the velocity" at these two points:

1) When it is at maximum displacement from the vertical

2) When it passes through the vertical displacement.To give a full answer one could consider its energy. The total energy is a sum of the Kinetic and Potential energy, these must always be conserved. At the maximum displacement it changes direction, therefore at some instant it must speed=0.

At the point it passes through the vertical it is the "lowest" point, so will have the minimum potential energy. Therefore it must have the maximum kinetic energy, hence maximum velocity. Therefore you must only work out where it will have half this value.
 

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