Derivative: position, velocity, acceleration as functions of time?

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SUMMARY

The discussion focuses on the dynamics of a 1.00 kg glider attached to a spring with a force constant of 25.0 N/m, oscillating on a frictionless air track. The initial conditions specify that at t = 0, the glider's velocity is -0.150 m/s, indicating it is moving towards the spring's compression. The key equations for position, velocity, and acceleration as functions of time in harmonic motion are derived from the principles of simple harmonic motion, specifically using the formulas for angular frequency and phase angle adjustments based on initial conditions.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with derivatives in calculus
  • Knowledge of oscillatory systems and spring constants
  • Ability to apply Newton's second law to dynamic systems
NEXT STEPS
  • Study the equations of motion for simple harmonic oscillators
  • Learn how to derive position, velocity, and acceleration functions from initial conditions
  • Explore the concept of angular frequency in oscillatory systems
  • Practice problems involving mass-spring systems and their dynamics
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Students in physics, particularly those studying mechanics, as well as educators and tutors looking to clarify concepts related to oscillatory motion and derivatives in real-world applications.

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Derivative: position, velocity, acceleration as functions of time?

Homework Statement



A 1.00 kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is passing through its equilibrium position with a velocity vx = - 0.150 m/s. (The negative sign means that the glider is headed in the direction which will compress the spring.)

Find the position, velocity, and acceleration as functions of time. Include units. Think carefully about the initial phase.


Homework Equations





The Attempt at a Solution



I am really stuck here. I am not sure how to get started with this question. Thanks for any hints or help anyone can provide.
 
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provide relevant eqns and draw a picture sometimes that helps.
 

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