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

An underdamped harmonic oscillator with mass m, spring constant k, and damping resistance c is subject to an applied force F0cosωt.

(a) [analytical] If, at t = 0, x = x0 and v = v0, what is x(t)?

2. Relevant equations

Ωinitial = √(k/m)

3. The attempt at a solution

Fnet = -kx - cv + F0cos(Ωt) = ma

x(t) = xh(t) (homogeneous) + xi(t) (inhomogeneous) so we will only be left with the inhomogeneous part

x(t) = Acos(Ωt - ∅)

A = (F0/m) / ((√(Ωinitial^2 - Ω^2)^2 + 4gamma*Ω^2))

∅ = tan-1((2*gamma*Ω)/(Ωinitial^2 - Ω^2))

I have all that but I am confused where x = x0 amd v = v0 come into play and how to plug it all into a x(t) equation

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Underdamped Harmonic oscillator with applied force

**Physics Forums | Science Articles, Homework Help, Discussion**