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(c) A 5.0 kg object oscillates on a spring with a spring constant of 180 N/m. The damping constant is 0.20 kg/s. The system is driven by a sinusoidal force of maximum value 50 N and an angular frequency of 20 rad/s. i) Determine the amplitude and phase lag of the oscillations. ii) If the driving frequency is varied, at what frequency will resonance occur? iii) Determine the maximum amplitude the system could possibly have. 2) A mass m is subject to a resistive force -bv and a driving force given by F = F_0 cos(w_d t). No restoring forces act on this system. a. Develop the differential equation of motion. b. By assuming a steady-state solution of the form x(t) = A cos(w_d t - delta) and using the complex exponential method, determine the amplitude A and phase lag delta for this system.

          (c) A 5.0 kg object oscillates on a spring with a spring constant of 180 N/m. The damping constant is 0.20 kg/s. The system is driven by a sinusoidal force of maximum value 50 N and an angular frequency of 20 rad/s.

i) Determine the amplitude and phase lag of the oscillations.
ii) If the driving frequency is varied, at what frequency will resonance occur?
iii) Determine the maximum amplitude the system could possibly have.

2) A mass m is subject to a resistive force -bv and a driving force given by F = F_0 cos(w_d t). No restoring forces act on this system.

a. Develop the differential equation of motion.

b. By assuming a steady-state solution of the form x(t) = A cos(w_d t - delta) and using the complex exponential method, determine the amplitude A and phase lag delta for this system.

(c) A 5.0 kg object oscillates on a spring with a spring constant of 180 N/m. The damping constant is 0.20 kg/s. The system is driven by a sinusoidal force of maximum value 50 N and an angular frequency of 20 rad/s.

i) Determine the amplitude and phase lag of the oscillations.
ii) If the driving frequency is varied, at what frequency will resonance occur?
iii) Determine the maximum amplitude the system could possibly have.

2) A mass m is subject to a resistive force -bv and a driving force given by F = F0 cos(wd t). No restoring forces act on this system.

a. Develop the differential equation of motion.

b. By assuming a steady-state solution of the form x(t) = A cos(wd t - delta) and using the complex exponential method, determine the amplitude A and phase lag delta for this system.

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