If in addition an external force is applied to the mass, and if the force varies according to a function of the form \(a\cos(\omega t) +b\sin(\omega t)\), then the long term behavior will be a simple ...If in addition an external force is applied to the mass, and if the force varies according to a function of the form \(a\cos(\omega t) +b\sin(\omega t)\), then the long term behavior will be a simple oscillation determined by the steady state part of the general solution; the initial position of the mass will not matter.
If the only force on the mass is due to the spring, then the behavior of the system is a damped oscillation. If in addition an external force is applied to the mass, and if the force varies according ...If the only force on the mass is due to the spring, then the behavior of the system is a damped oscillation. If in addition an external force is applied to the mass, and if the force varies according to a function of the form \( a\cos(\omega t)+b\sin(\omega t)\), then the long term behavior will be a simple oscillation determined by the steady state part of the general solution; the initial position of the mass will not matter.
