Find max energy stored in oscillating system

AI Thread Summary
The discussion focuses on calculating the maximum energy stored in a spring-mass oscillating system described by the equation x = 0.090cos(2.90t). The spring constant k was determined to be 7.569, leading to a displacement x of 1.165 meters. Participants confirm that the total energy can be calculated using the formula 1/2kx^2, given the values of k and x. For the maximum velocity of the mass, the equation v = -Aω sin(ωt) is suggested for use. The conversation emphasizes the importance of correctly applying these formulas to solve for energy and velocity in oscillatory motion.
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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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