The solution of the underdamped harmonic oscillator is (x(t)=) (A e^{-beta t} cos left(omega_{1} t+varphiight)), where (omega_{1}=sqrt{omega_{0}^{2}-beta^{2}}).

Question:

The solution of the underdamped harmonic oscillator is \(x(t)=\) \(A e^{-\beta t} \cos \left(\omega_{1} t+\varphiight)\), where \(\omega_{1}=\sqrt{\omega_{0}^{2}-\beta^{2}}\). Find the arbitrary constants \(A\) and \(\varphi\) in terms of the initial position \(x_{0}\) and initial velocity \(v_{0}\).

Fantastic news! We've Found the answer you've been seeking!