A mass, M = 1.75 kilogram, is attached to a wall by a spring with k = 583 N/m. The mass slides on a frictionless floor. The spring and mass are immersed in a fluid with a damping constant of 6.43 kg/s. A horizontal force, F(t) = Fdcos(dt), where Fd = 53.7 Newton, is applied to the mass through a knob, causing the mass to oscillate back and forth. Ignore the mass of the spring and of the knob and rod.
a) Find at what frequency will the amplitude of the mass' oscillation be greatest?
b) Evaluate what is the maximum amplitude?
c) If the driving frequency is reduced slightly (but the driving amplitude remains the similar), find at what frequency will the amplitude of the mass' oscillation be half of the maximum amplitude?