Finding total energy of an oscillator

AI Thread Summary
To find the total energy of the oscillator with mass m = 2 kg and displacement x(t) = 2cos(6πt), the angular frequency ω is crucial, which is 6π rad/s. The maximum speed is calculated as v(max) = Aω, resulting in v(max) = 2 * 6π = 12π m/s. The kinetic energy (KE) at maximum speed is KE = 1/2 * m * v(max)², leading to KE = 1/2 * 2 * (12π)². The total energy in simple harmonic motion is equal to the maximum kinetic energy, which is approximately 1440 J, aligning closely with option B) 1420.
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Homework Statement



Find the total energy of the following (mass m= 2 kg) oscillator.

Homework Equations



x=2cos(6∏t)


The Attempt at a Solution



Wouldn't I take my Amplitude of 2 and my period of 6 mulitply them together to get my max velocity of 12 then using KE = 1/2msquared I would take 1/2(2)(12)squared to get 144. But this is no where close to being right. My choice are:

A) 1320
B) 1420
C) 1520
D) 1620
E) 1720
F) 1820
 
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The simple harmonic motion is described with a function x(t)=Acos(ωt), with ω the angular frequency. The maximum speed is v(max)=Aω. You need ω. What is it if x(t)=2cos(6π t)?

ehild
 

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