Simple Harmonic Motion is essentially a model for some basic oscillating movements. Eg. A pendulum, a block suspended by a spring, a block on a frictionless table connected to a fixed position by a spring. It is the basis for a whole lot of Physics concerning position vs velocity vs acceleration, kinetic and potential energy, etc.

The single most important thing when it comes to Simple Harmonic Motion (SHM), is the fact that acceleration is always directly proportional to displacement, and directed towards the centre point of equilibrium.

ie. acceleration (proportional to) -displacement

Also, it should be noted that a pendulum does not itself execute SHM. Only when you take a projection of the motion, in the plane generated by the equilibrial line of the motion, and the line perpendicular to this line, and also perpendicular to the motion of the pendulum... only then will the bottom of the pendulum appear to be executing SHM! In simple terms, if you have a pendulum on a string, and shine a light onto it sideways and place a screen behind, the shadow of the mass on your screen will appear to be executing SHM, going up and down, while the string appears to stay in the same place, only getting longer and shorter, as if by magic.

/msg me if you know the ascii code for the proportianlity sign. I couldnt find anything.

A body undergoing simple harmonic motion is freely oscillating about a point of equilibrium, with a restoring force proportional to its displacement.

The displacement of the body at a time t is its distance from the point of equilibrium. Since it is continually moving, its displacement is always changing and so the magnitude of the restoring force is changing too. It is "restoring" in the sense that it is acting to move the body back toward equilibrium, so while moving away from equilibrium, the body at first decelerates, briefly stops at its maximum displacement, and then heads back the other way, and starts the process in the opposite direction. It is going fastest as it passes through equilibrium and slowest when it briefly stops while at maximum displacement.

At a time t, the acceleration, a, of a body undergoing SHM can be calculated by a = - (2π f)2 x, where f = frequency (oscillations per second) and x = displacement. Note the minus sign in the equation.

This displacement x is calculated by either

x = A sin (2π f t) if the oscillation started at equilibrium (i.e. it can be represented on a sine curve),

or x = A cos (2π f t) if the oscillation started at maximum displacement (it can be represented on a cosine curve).

In both cases, A is the amplitude of the oscillation - its maximum displacement. Do not confuse A, amplitude, with a, acceleration.

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