Lecture D32: Damped free vibration Spring-Dashpot-Mass System C Spring force Fs=ka k>0 Dashpot Fd=-ca C>0 Newton's Second Law(mi=2F) m+ ca+k =0 (Define )Natural Frequency wn=vk/m,and Period T=2T/Wn (Define)Damping Factor s=c/(2mwn) Equation of motion +2(um+u2m=0Lecture D32 : Damped Free Vibration Spring-Dashpot-Mass System Spring Force Fs = −kx, k > 0 Dashpot Fd = −cx˙, c > 0 Newton’s Second Law (mx¨ = P F) mx¨ + cx˙ + kx = 0 (Define) Natural Frequency ωn = q k/m, and Period τ = 2π/ωn (Define) Damping Factor ζ = c/(2mωn) Equation of motion x¨ + 2ζωnx˙ + ω 2 nx = 0 1