Spring-Mass Problem: Natural Frequency Calculation

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SUMMARY

The natural frequency of a spring-mass system can be calculated using the formula T = 2π√(m/k). In this discussion, a weight compressing a vertical spring by 2.5 cm leads to a calculated natural frequency of 3.15 s-1. The displacement was confirmed to be in meters, using the standard gravitational acceleration of 9.81 m/s2. The calculations and units used in the solution were validated by forum participants.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with the concept of natural frequency in oscillatory systems
  • Basic knowledge of gravitational acceleration (g = 9.81 m/s2)
  • Ability to manipulate algebraic equations
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  • Research the derivation of the formula T = 2π√(m/k)
  • Explore the effects of varying mass and spring constant on natural frequency
  • Learn about damping in spring-mass systems
  • Investigate real-world applications of spring-mass oscillations in engineering
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Students studying physics, engineers working with mechanical systems, and anyone interested in understanding oscillatory motion in spring-mass systems.

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Homework Statement


A weight (unknown mass) is placed on a vertical spring (unknown spring constant) compressing it by 2.5 cm (one inch). What is the natural frequency of oscillation of this spring-mass system?


Homework Equations


(i) T = 2*pi*\sqrt{\frac{m}{k}}



The Attempt at a Solution


I argue that the spring's displacement should be \frac{mg}{k} = 0.025
So \frac{m}{k} = \frac{0.025}{g}
Plugged that in and got the natural frequency is 3.15 s^-1.

I just want to check if the equations are valid and if the displacement is in the right unites (meters, right?)
 
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Looks good. (What value did you use for g?)
 
Oh, good call. I used 9.81, so it's in meters.
 

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