One end of an ideal spring is attached to the wall and other free end to a particle sized block (no friction). If a push is given to the block, will it go on oscillating about the equilibrium position? I am thinking of this considering Law of conservation of energy.
Friction acts as a "damping force" for a harmonic oscillator. It is usually assumed proportional to the instantaneous velocity, and contributes to the instantaneous force as such. If one solves the differential equation for the displacement of the particle about the equilibrium position after adding a term proportional to the velocity to the usual equation for a harmonic oscillator, one gets a sinusoidal function of time, whose amplitude decreases exponentially with time- i.e. the amplitude goes ever closer to zero, reaching zero at infinite time. Realistically, this means that it has to stop after some finite time. Why? Because our capabilities for measurement are limited by some resolution; that is, we cannot measure distances lesser than some very small length measurable by the most powerful length-measuring instrument in the world. And so, for all intents and purposes, the block becomes stationary at the time its amplitude dips below this small distance. Interestingly, quantum mechanics tells us that the constituent particles are never stationary, and keep oscillating even at zero kinetic energy- but this oscillation is different.