## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) The period is time taken to complete one cycle. This is $$\frac{33s}{10 oscillations}=3.3s/oscillation$$ Therefore, $T=3.3s$. (b) The frequency is equal to $$f=\frac{1}{T}$$ Substituting the value of $T=3.3s$ yields a frequency of $$f=\frac{1}{3.3s}=0.30Hz$$ (c) The angular frequency $\omega$ equals $\omega=2\pi f$. Substituting $f=0.30Hz$ yields $\omega=2\pi(0.30Hz)=1.9rad/s$ (d) The amplitude is the distance from equilibrium to maximum compression. Since the minimum and maximum distance are separated by $50cm$, the amplitude must be half of this value, $25cm$. (e) The maximum speed of an oscillator equals $v_m=A\omega$. Substituting known values of $A=25cm$ and $\omega=1.9rad/s$ yields a maximum speed of $$v_m=(25cm)(1.9rad/s)=48cm/s$$