Problem 8.51 Challenge

a) กำหนดให้ \(m = 0.250 kg, k = 25.0 N/m\) และ \(b = 0.300 kg/s\)

จาก \(γ = \frac{b}{2m} = 0.600 Hz\) และ \(ω_{0} = \sqrt{\frac{k}{m}}= 10.0 Hz\)

จาก \(\gamma < \omega _{0}\)

∴ เป็นการสั่นแบบ \(Underdamped \;\blacksquare\)

b) จาก \(ω = \sqrt{\omega _{0}^{2} - \gamma ^{2}}\)

\(2\pi f =\sqrt{\omega _{0}^{2} - \gamma ^{2}}\)

\(f =\frac{1}{2\pi}\sqrt{\omega _{0}^{2} - \gamma ^{2}}= 1.59 Hz \;\blacksquare\)

c) จาก \(ω = \sqrt{\omega _{0}^{2} - \gamma ^{2}}\)

\(\frac{2\pi}{T}=\sqrt{\omega _{0}^{2} - \gamma ^{2}}\)

\(T =\frac{2\pi}{\omega _{0}^{2} - \gamma ^{2}}= 0.630 s \;\blacksquare\)

\(_{-\gamma t}\)

d) จาก \(A(t) = Ae\)

\(_{-\gamma (0)}\)

\(20.0 cm = Ae\)

\(A = 20.0 cm\)

\(_{-(0.600 Hz)(5.00 s)}\)

จะได้ \(A(5.00) = (20.0 cm)e= 1.00 cm \;\blacksquare\)