How Do You Solve a Damped Harmonic Oscillator Differential Equation?

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To solve the damped harmonic oscillator differential equation, one must first identify the distinct roots (k1, k2) from the characteristic equation k^2 + 2Bk + w^2 = 0. The general solution is expressed as x(t) = Ae^(k1t) + Be^(k2t). To find k1 and k2, solving the quadratic equation is essential. The discussion emphasizes the need for guidance on how to approach the problem, particularly in deriving the roots. Understanding this process is crucial for effectively solving the differential equation.
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damped harmonic oscillator, urgent help needed!

Homework Statement



for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0


Homework Equations





The Attempt at a Solution



I have no idea where to begin, can anyone point me in the right direction or giv me some sort of outline to follow
 
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I would first find k1 and k2. This involves solving the quadratic equation you were given.
 

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