All Problems

Mechanical Oscillations

Problem 4.4

Find the angular frequency and the amplitude of harmonic oscillations of a particle if at distances \(x_{1}\) and \(x_{2}\) from the equilibrium position its velocity equals \(v_{1}\) and \(v_{2}\) respectively.

Reveal Answer
ω=(v12−v22)/(x22−x12);a=(v12x22−v22x12)/(v12−v22)\omega=\sqrt{\left(v_{1}^{2}-v_{2}^{2}\right) /\left(x_{2}^{2}-x_{1}^{2}\right)} ; a=\sqrt{\left(v_{1}^{2} x_{2}^{2}-v_{2}^{2} x_{1}^{2}\right) /\left(v_{1}^{2}-v_{2}^{2}\right)}
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