Amplitude and period of a spring

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SUMMARY

The discussion focuses on calculating the period of a spring-mass system in simple harmonic motion, specifically with a 340 g mass that displaces the spring by 30 cm. The relevant equations include the angular frequency formula, ω = √(k/m), and the relationship between angular frequency and frequency, ω = 2πf. The user expresses confusion about the amplitude and the spring constant, indicating a need for clarity on how these factors influence the period of motion.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the spring constant (k) and mass (m) relationship
  • Knowledge of angular frequency (ω) and its calculation
  • Basic grasp of energy conservation in mechanical systems
NEXT STEPS
  • Study the derivation of the period formula for spring-mass systems
  • Learn how to calculate the spring constant (k) using Hooke's Law
  • Explore the relationship between amplitude and energy in simple harmonic motion
  • Investigate the effects of mass on the frequency of oscillation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to springs and harmonic motion.

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Homework Statement


A 340 g mass is attached to a vertical spring and lowered slowly until it rests at a new equilibrium position, which is 30 cm below the spring's original equilibrium. The spring is then set into simple harmonic motion. What is the period of the motion?


Homework Equations


I don't know how to enter greek letters, so let w=omega
x(t)=Acos(wt)
w=sqrt(k/m)
w=2pi*f

The Attempt at a Solution


I tried it using conservation of energy, but that didn't really help because v has many extra variables in its equation. Does the addition of the mass cause a 30 cm increase in the amplitude, or is it only half? I just thought of something. If I knew how to relate the angular frequencies, I could use conservation of energy, but I don't know how to relate the angular frequencies.
 
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Do you know how the spring constant is defined?

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