An oscillating spring with mass

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SUMMARY

The discussion focuses on the oscillatory motion of a 1.00 kg glider attached to a spring with a force constant of 49.0 N/m on a frictionless air track. The period of the motion is calculated using the formula T = 2π√(M/k), resulting in a period of 2.70 seconds. The maximum speed and acceleration, as well as the position, velocity, and acceleration as functions of time, are key components to be determined for a complete analysis of the system's dynamics.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with simple harmonic motion concepts
  • Knowledge of basic calculus for deriving functions of motion
  • Ability to apply Newton's second law in oscillatory systems
NEXT STEPS
  • Calculate maximum speed using the formula v_max = Aω, where A is amplitude and ω is angular frequency.
  • Determine maximum acceleration using the formula a_max = Aω².
  • Derive position, velocity, and acceleration functions using x(t) = A cos(ωt + φ), v(t) = -Aω sin(ωt + φ), and a(t) = -Aω² cos(ωt + φ).
  • Explore the effects of damping on oscillatory motion in real-world applications.
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone studying dynamics and oscillatory systems will benefit from this discussion.

jenha14
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A 1.00 kg glider attached to a spring with a force constant 49.0 N/m oscillates on a horizontal, frictionless air track. At t = 0, the glider is released from rest at x = -2.7 cm. (That is, the spring is compressed by 2.7 cm.)
(a) Find the period of its motion.
(b) Find the maximum values of its speed and acceleration.
(c) Find the position, velocity, and acceleration as functions of time (t).


I used the equation T = 2(pi)*sqrt(M/k) to find the period of motion, but I don't known what to use for (b) or (c)
 
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Don't they give you the period in the question? It says "a period of 2.70 s".
 

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