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10 Nov 2019
Consider damped harmonic oscillation. Newton's Second Law leads to the differential equation x + 2 delta x + omega2 x = 0. In the critically damped case delta2 = omega2. Show that e and the are elementary functions which satisfy this equation and find the condition for lambda. A linear combination of the two elementary function is the general solution. Find the general solution for a critically damped mass with the initial displacement x0 and initial velocity v0 at t = 0.
Consider damped harmonic oscillation. Newton's Second Law leads to the differential equation x + 2 delta x + omega2 x = 0. In the critically damped case delta2 = omega2. Show that e and the are elementary functions which satisfy this equation and find the condition for lambda. A linear combination of the two elementary function is the general solution. Find the general solution for a critically damped mass with the initial displacement x0 and initial velocity v0 at t = 0.