I have a question about the Expert solution posted to thefollowing problem: At w
ID: 1749479 • Letter: I
Question
I have a question about the Expert solution posted to thefollowing problem: At what displacement of a simple harmonic oscillator is theenergy half kinetic and half potential? The solution seems to follow a logical progression, lookingfor both the kinetic energy and potential energy, but I don'tunderstand it. Here's how they begin solving this: Kinetic energy: 1/2mv2 (KE)1 =1/2mw2(A3-x2) **where does thiscome from? They don't define the variables used (I know A isamplitude, and is angular velocity, but what isw?). The remainder of the solution made complete sense and let tothe correct answer, but can someone help me understand this keystep? Thanks!! I have a question about the Expert solution posted to thefollowing problem: At what displacement of a simple harmonic oscillator is theenergy half kinetic and half potential? The solution seems to follow a logical progression, lookingfor both the kinetic energy and potential energy, but I don'tunderstand it. Here's how they begin solving this: Kinetic energy: 1/2mv2 (KE)1 =1/2mw2(A3-x2) **where does thiscome from? They don't define the variables used (I know A isamplitude, and is angular velocity, but what isw?). The remainder of the solution made complete sense and let tothe correct answer, but can someone help me understand this keystep? Thanks!! (KE)1 =1/2mw2(A3-x2) **where does thiscome from? They don't define the variables used (I know A isamplitude, and is angular velocity, but what isw?). The remainder of the solution made complete sense and let tothe correct answer, but can someone help me understand this keystep? Thanks!!Explanation / Answer
to find out when potential and kinetic energy are equal we need toknow when 1/2 k x2 (potential energy) is equal to halfthe total energy of the system, the total energy of a spring systemis given by the formula 1/2 k A2 so we want to know when 1/2 k x2 = 1/2 (1/2 kA2) x2 = 1/2 A2 x = A/4 this is alot simpler than the experts solution
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