Calculating Time to Reach 1/2x from Equilibrium for a Mass & Spring

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SUMMARY

The discussion focuses on calculating the distance from equilibrium at which a mass-spring system experiences acceleration equal to half its maximum acceleration. The correct distance is determined to be 1/2x, where x represents the distance the spring is stretched from its equilibrium position. Additionally, when a mass of 2.62 kg stretches a spring 0.315 m and is then stretched an additional 0.130 m, the new equilibrium position is established at 0.445 m. To calculate the time to reach this new equilibrium, the spring constant is required.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of simple harmonic motion principles
  • Familiarity with mass-spring systems
  • Basic calculus for time period calculations
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  • Research the derivation of the formula for acceleration in mass-spring systems
  • Learn how to calculate the spring constant using Hooke's Law
  • Explore the concept of equilibrium positions in oscillatory motion
  • Study the time period of oscillation for different mass-spring configurations
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Physics students, mechanical engineers, and anyone studying dynamics of oscillatory systems will benefit from this discussion.

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1. A mass attached to the end of a spring is stretched a distance x from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

My answer was 1/2A, but the correct answer was 1/2x, I don't know if there is a difference between these two. But I mean x may not be the amplitude, but I think the answer should be the half of its Amplitude.

2. A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?

Here, what does it mean by new equilibrium position? 0.315m is the equilibrium point?

Thanks for help.
 
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The correct answer to your first question is 1/2x, where x is the distance the spring is stretched from its equilibrium position. The new equilibrium position in the second question would be 0.445m (the original equilibrium position plus 0.130m). To find the time it takes for the mass to reach the new equilibrium position, you would need to know the spring constant for the spring.
 

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