Simple Harmonic Motion-Period of oscillations

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SUMMARY

The period of oscillations for a mass-spring system is calculated using the formula T = 2π/ω, where ω is derived from ω = √(k/m). In this case, with a mass of 10 kg and a spring constant of 20 N/m, the angular frequency ω is determined to be 1.41 rad/s. Consequently, the period T is calculated to be approximately 4 seconds when rounded to one significant figure, consistent with the precision of the given values.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with the concepts of mass and spring constants
  • Ability to manipulate algebraic equations
  • Knowledge of significant figures in measurements
NEXT STEPS
  • Study the derivation of the period formula for Simple Harmonic Motion
  • Explore the effects of varying mass and spring constant on oscillation periods
  • Learn about energy conservation in mass-spring systems
  • Investigate damping effects on oscillations in SHM
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to Simple Harmonic Motion.

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Homework Statement



What is the period of oscillations of a spring fixed to the ceiling at one end and set in motion by attaching a mass 10kg to the other end? The spring constant is 20 N/m.

Homework Equations



I used equations found in my lab book for Simple Harmonic Motion.

ω=√k/m

Then I used the equation ω=2pi/T to solve for T


The Attempt at a Solution



I used equations found in my lab book for Simple Harmonic Motion.
First I found
ω according to ω=√k/m
ω=√20/10
ω=√2
ω=1.41

Then I used the equation ω=2pi/T to solve for T
1.41 = 2pi/T
1.41(T)=2pi
T=2pi/1.41
T=4
I rounded T to only 1 significant figure, the same as the given mass and spring constant.

I have a final answer (4) but I am not sure I did this problem correctly, and I am unsure of my algebra where I solved for T. Also, would it be rounded to 1 significant figure?
Any insight would be great. Thanks!
 
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