Doubling Period and Amplitude: Object's Maximum Speed

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SUMMARY

The discussion centers on the effects of doubling both the amplitude and the period of an object in simple harmonic motion on its maximum speed. It is established that the maximum speed remains unchanged despite the doubling of both parameters. The relationship is defined by the formula max v = Aω, where ω is the angular frequency inversely related to the period. Thus, while the amplitude increases, the period's effect on angular frequency compensates, resulting in a constant maximum speed.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the formula max v = Aω
  • Knowledge of angular frequency and its relationship to period
  • Basic concepts of pendulum motion
NEXT STEPS
  • Study the derivation of the formula max v = Aω in detail
  • Explore the relationship between period and angular frequency in simple harmonic motion
  • Investigate the effects of varying amplitude on maximum speed in different oscillatory systems
  • Learn about energy conservation in simple harmonic motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of oscillatory motion will benefit from this discussion.

yahoo32
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An ob ject moves with simple harmonic motion. If the amplitude and
the period are both doubled, the ob ject’s maximum speed is


I believe the object's maximum speed would be halved correct? Considering the regular velocity does not depend on the Amplitude and only the Period would affect it?
 
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Hi yahoo32! :smile:

Thanks for the PM.
yahoo32 said:
I believe the object's maximum speed would be halved correct? Considering the regular velocity does not depend on the Amplitude and only the Period would affect it?

Hint: Think of a pendulum.

Double the amplitude … what happens to the maximum velocity? :smile:
 
Ahhh! So max v = A w . Therefore doubling T and A will keep the max velocity the same, correct?
 
:biggrin: Harmony is restored! :biggrin:​
 

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