(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the general solution of the damped SHM equation(5.9) for the special case of critical damping , that is , when K = [tex]\Omega[/tex]. Show that , if the particle is initially relaeased from rest at x= a , then the subsequent motion is given by

x=a*(e^-([tex]\Omega[/tex]*t))*(1+[tex]\Omega[/tex]*t)

2. Relevant equations

x''+2Kx'+([tex]\Omega[/tex])^{2}*x=0

x=A*cos([tex]\Omega[/tex]*t) + B*sin([tex]\Omega[/tex]*t)

3. The attempt at a solution

x=e^{[tex]\lambda[/tex]*t}

x'= [tex]\lambda[/tex]*e^{[tex]\lambda[/tex]*t}

x''=[tex]\lambda[/tex]^{2}*e^{[tex]\lambda[/tex]*t}

x'= -A*[tex]\Omega[/tex]*sin([tex]\Omega[/tex]*t) + B*[tex]\Omega[/tex]*cos([tex]\Omega[/tex]*t)

x''= -A*[tex]\Omega[/tex]^{2}*cos([tex]\Omega[/tex]*t) - B*[tex]\Omega[/tex]^{2}*sin([tex]\Omega[/tex]*t)

Not sure how to proceed...

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# Homework Help: Critical Damped motion

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