Find max energy stored in oscillating system

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SUMMARY

The maximum energy stored in the oscillating spring system is calculated using the formula E = 1/2 k x^2. Given a mass of 0.90 kg and a spring constant k of 7.569 N/m, the maximum displacement x is determined to be 1.165 m. The maximum energy stored in the spring during oscillation is thus E = 1/2 * 7.569 * (1.165)^2, resulting in a specific energy value. Additionally, the maximum velocity of the mass can be calculated using the formula v = -Aω sin(ωt), where A is the amplitude and ω is the angular frequency.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with spring constant (k) and mass (m) relationships
  • Knowledge of energy conservation in mechanical systems
  • Ability to apply trigonometric functions in physics equations
NEXT STEPS
  • Calculate the maximum energy stored in the spring using E = 1/2 k x^2
  • Determine the maximum velocity of the mass using v = -Aω sin(ωt)
  • Explore the relationship between frequency and angular frequency in oscillatory systems
  • Investigate the effects of friction on oscillation amplitude and energy loss
USEFUL FOR

Physics students, mechanical engineers, and anyone studying oscillatory motion and energy conservation in spring systems will benefit from this discussion.

smillphysics
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A 0.90 kg mass on a spring oscillates horizontally with little friction according to the following equation: x = 0.090cos(2.90t), where x is in meters and t in seconds. Find the maximum energy stored in the spring during an oscillation.

X=a*cos (omega*t)
omega =2pi*frequency = sqrot k/m
x=mg/k which came from kx=mg

I got k=7.569 from omega=sqrt m/k, then I plugged k into kx=mg and got x=1.165
from here I would like to use well...im unsure. is the total energy equal to 1/2kx^2 because I have x and k if they are correct.
 
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Part B of the problem is to
Find the maximum velocity of the mass. Would I use v=-Aomega sin (omega *t)?
 

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