Harmonic motion (mass on a spring) follows the differential equation model -k*x = m*x'' (derivative with respect to time t) when there is no friction. This is based on Hooke's Law and Newton's Second Law, where m is the mass (in kg) and k is the spring constant (in N/m). A general solution to this second order differential equation is found, as well as a particular (unique) solution of an IVP, representing harmonic motion.. Then we add friction and get -b*x' - k*x = m*x''. With m=1, b=7, and k=12, we solve this differential equation and write a general solution.
Differential Equations for Calculus 2, Part 7B
#Calculus2 #DifferentialEquations #HarmonicMotion
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14 окт 2024
