Find Amplitude and Equilibrium in Simple Harmonic Motion

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SUMMARY

The discussion focuses on calculating key parameters of simple harmonic motion for a 0.241-kg particle oscillating between x1 = -0.349 m and x2 = 0.419 m with a period of 0.511 s. The equilibrium position (xeq) is determined using the midpoint formula, yielding xeq = (x1 + x2)/2 = 0.035 m. The amplitude (A) is calculated as half the distance between the two points, A = |x2 - x1|/2 = 0.384 m. The frequency (f) is derived from the period using the formula f = 1/T, resulting in a frequency of approximately 1.96 Hz.

PREREQUISITES
  • Understanding of simple harmonic motion concepts
  • Familiarity with the midpoint formula
  • Knowledge of oscillation period and frequency calculations
  • Ability to interpret physical parameters in motion equations
NEXT STEPS
  • Study the relationship between period and frequency in oscillatory systems
  • Explore the mathematical derivation of amplitude in simple harmonic motion
  • Learn about the implications of equilibrium position in mechanical systems
  • Investigate graphical representations of simple harmonic motion
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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.

jcd2012
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Homework Statement



A 0.241-kg particle undergoes simple harmonic motion along the horizontal x-axis between the points x1 = -0.349 m and x2 = 0.419 m. The period of oscillation is 0.511 s. Find the frequency, f, the equilibrium position, xeq, the amplitude, A.

Homework Equations



The hint system suggests:

Midpoint Formula: (X_1 + X_2)/2
Distance Between Two Points: |X_1 - X_2|

The Attempt at a Solution



I am just not sure how I get amplitude and equilibrium from this information. The hint system suggests that I draw the setup to determine these however I am lost from there.
 
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I would suggest you consider the definitions and equations of frequency, equilibrium and amplitude. After drawing the system, consider how these quantities are represented in the system.
 

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