Problem 8.7

จาก \(v = ω_{0}\sqrt{A^{2} - x^{2}}\)

\(v^{2} = \omega _{0}^{2}(A^{2} - x^{2})\)

จะได้ \(0.40^{2} = ω_{0}^{2}(A^{2} - 0.20^{2})\)

และ \(0.20^{2} = ω_{0}^{2}(A^{2} - 0.40^{2})\)

\(\therefore \frac{0.40^{2}}{0.20^{2}}=\frac{A^{2} - 0.20^{2}}{A^{2} - 0.40^{2}}\)

\(0.16A^{2} - 0.0256 = 0.040A^{2} - 0.0016\)

\(A^{2} = 0.20 m^{2}\)

\(\therefore 0.40^{2} = \omega _{0}^{2}(0.20 - 0.20^{2})\)

\(\omega _{0}^{2} = 1.0\)

\(|\omega _{0}| = 1.0 rad/s\)

จาก \(v = ω_{0}\sqrt{A^{2} - x^{2}}\)

\(v = (1.0 rad/s)\sqrt{(0.20 m^{2}) - (0.30 m)^{2}}\)

\(v = 0.33 m/s \;\blacksquare\)