Mon March 21, 2011 By: N Jain

in SHMrestoring force have max. magnitude at same instant but they are out of phase and point in opposite directions. HOW?/?

Expert Reply
Mon March 21, 2011
Dear student,
 Position and velocity are out of phase.  The velocity is zero at maximum displacement, and the displacement is zero at maximum speed. 

For simple harmonic motion, the acceleration a = -ω2x is proportional to the displacement, but in the opposite direction.  Simple harmonic motion is accelerated motion.  If an object exhibits simple harmonic motion, a force must be acting on the object.  The force is

F = ma = -mω2x .

It obeys Hooke's law, F = -kx, with k = mω2.

Any physical situation in which an object has a restoring force that is proportional to the displacement, as in Hooke's law, will produce simple harmonic motion. A physical situation that has a restoring force that does not follow Hooke's law will produce oscillatory motion that is not simple harmonic motion.

Hope this helps.
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