A horizontal mass–spring system has negligible damping. The spring constant is k=200Nm−1 and the attached mass is m=0.50kg. A small external driving force of constant amplitude can be adjusted to one of the following three angular frequencies:
ωd1=18rads−1,ωd2=20rads−1,ωd3=25rads−1.
(a) Calculate the natural angular frequency of the system.
(b) Identify which of the three driving frequencies will produce the maximum steady-state amplitude. Give a reason for your choice.
(c) If the driver is set to ωd=19rads−1 instead, state qualitatively whether the amplitude will be slightly smaller, much smaller, or almost the same as the amplitude obtained in part (b). Give one line of reasoning.