A 1 kg mass is suspended on a spring with spring constant 4 N/m. The system...

Transcribed Image Text:

A 1 kg mass is suspended on a spring with spring constant 4 N/m. The system is damped with unspecified damping coefficient b>0. The spring is initially at rest (i.e. no displacement from equilibrium and no initial velocity). An external force is applied to the damped mass-spring system given by F(t) = 8cos(2t). (a) Set up the damped mass-spring equation with the corresponding initial condition. (b) Solve for the steady-state solution. (c) Describe how the dampening coefficient, b, influences the amplitude of the oscillation. (d) Describe what would happen if the system were undamped, i.e. b=0. A 1 kg mass is suspended on a spring with spring constant 4 N/m. The system is damped with unspecified damping coefficient b>0. The spring is initially at rest (i.e. no displacement from equilibrium and no initial velocity). An external force is applied to the damped mass-spring system given by F(t) = 8cos(2t). (a) Set up the damped mass-spring equation with the corresponding initial condition. (b) Solve for the steady-state solution. (c) Describe how the dampening coefficient, b, influences the amplitude of the oscillation. (d) Describe what would happen if the system were undamped, i.e. b=0.