Question

The position of a mass on a spring is given by x = (8.0 cm) cos [2 π t / (0.96 s)].

a) What is the period, T, of this motion?
b) Where is the mass at t = 3.9 s?

Answer 1

\[x(t) = 8 \cos \frac{2 π }{0.96}t\]
Compair with\[x(t) = A\cos(ωt + φ)=A\cos(2\pi ft + φ)=A\cos\left(\frac{2\pi }Tt + φ\right)\]where
\(A\) is the amplitude

\(\omega\) is the angular frequency

the frequency is \(f=\frac{\omega}{2\pi}\)

the period is \(T=\frac1{f}=\frac{2\pi}\omega\)

\( φ \) is the phase lag