How Do You Calculate Maximum Acceleration of a Simple Harmonic Oscillator?

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SUMMARY

The maximum acceleration of a simple harmonic oscillator can be calculated using the formula a(max) = Aω², where A is the amplitude and ω is the angular frequency. Given an amplitude of 0.49 m and a period of 3.7 seconds, the angular frequency is determined using the equation ω = 2π/T, resulting in ω = 1.698 rad/s. Substituting these values into the maximum acceleration formula yields a maximum acceleration of 0.0358 m/s².

PREREQUISITES
  • Understanding of simple harmonic motion concepts
  • Familiarity with the formulas for angular frequency and maximum acceleration
  • Basic knowledge of trigonometric functions, specifically π
  • Ability to perform unit conversions and calculations
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  • Study the derivation of the maximum acceleration formula a(max) = Aω²
  • Learn how to calculate angular frequency using different periods
  • Explore the relationship between amplitude, period, and frequency in harmonic motion
  • Investigate real-world applications of simple harmonic oscillators in physics
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for clear examples of simple harmonic oscillators.

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Homework Statement


A simple harmonic oscillator has amplitude 0.49 m and period 3.7 sec.
What is the maximum acceleration?


Homework Equations


a(max)=Aw^2
w=angular frequency
Vmax=Aw
w= angular frequency


The Attempt at a Solution



I attempted to divide the Amplitude (.49m) by the time (3.7 sec) in order to find the maximum velocity. Plugging this value (.132432m/s) into the maximum velocity equation (Vmax=Aw) to solve for w I got a value of .27027027 which I plugged into the maximum acceleration equation to get a value of .035792549. Which was wrong
 
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w =2π/T
T:period.
i think you can find w with this equation.
 
That worked, thank you very much
 

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