Period of oscillation for a mass on a spring

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SUMMARY

The period of oscillation for a mass on a spring is influenced by the mass attached to the spring, contrary to the behavior observed in a simple pendulum where mass is less significant. The amount of spring deflection is directly proportional to the attached mass, leading to shorter oscillation periods for smaller masses. However, the amplitude of oscillation does not depend on the mass but rather on the initial conditions. In a mass-spring system, the equilibrium deflection is determined by the mass, but this does not correlate with the amplitude or the period of oscillations.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of oscillatory motion and periods
  • Familiarity with concepts of equilibrium in mechanical systems
  • Knowledge of initial conditions in physical systems
NEXT STEPS
  • Study Hooke's Law and its application in mass-spring systems
  • Explore the mathematical derivation of the period of oscillation for springs
  • Investigate the differences between mass-spring systems and simple pendulums
  • Learn about the effects of damping on oscillatory motion
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Physics students, mechanical engineers, and anyone interested in understanding the dynamics of oscillatory systems and their applications in real-world scenarios.

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Why does the period of oscillation for a mass on a spring depend on its mass? (while in other situations, like a simple pendulum, the mass seems to be unimportant)
 
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Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.
 
because the restoring force for a pendulum is due to gravity
for a larger mass the restoring force is automatically larger.
that is not the case for a mass-spring system
 
hotvette said:
Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.
This is a little confusing and mostly not true.
The period does not depend on the spring deflection (amplitude) and the amplitude does not depend on the mass attached but on the initial conditions.
If you have in mind a vertical spring (it does not have to be vertical) with a mass attached, then the mass determines the equilibrium deflection, but this is not in general related to the amplitude or the period of the oscillations.
 

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