Introduction Simple_harmonic_motion

simple harmonic motion shown both in real space , phase space. orbit periodic. (here velocity , position axes have been reversed standard convention align 2 diagrams)

in diagram, simple harmonic oscillator, consisting of weight attached 1 end of spring, shown. other end of spring connected rigid support such wall. if system left @ rest @ equilibrium position there no net force acting on mass. however, if mass displaced equilibrium position, spring exerts restoring elastic force obeys hooke s law.

mathematically, restoring force f given by

f

=
−
k

x

,


{\displaystyle \mathbf {f} =-k\mathbf {x} ,}

where f restoring elastic force exerted spring (in si units: n), k spring constant (n·m), , x displacement equilibrium position (m).

for simple mechanical harmonic oscillator:

when system displaced equilibrium position, restoring force obeys hooke s law tends restore system equilibrium.

once mass displaced equilibrium position, experiences net restoring force. result, accelerates , starts going equilibrium position. when mass moves closer equilibrium position, restoring force decreases. @ equilibrium position, net restoring force vanishes. however, @ x = 0, mass has momentum because of acceleration restoring force has imparted. therefore, mass continues past equilibrium position, compressing spring. net restoring force slows down until velocity reaches zero, whereupon accelerated equilibrium position again.

as long system has no energy loss, mass continues oscillate. simple harmonic motion type of periodic motion.