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Define the terms "acceleration" and "displacement". Explain simple harmonic motion with reference to both of these quantities.

Firstly, acceleration is the rate of change of velocity of an object, measured in ms-2 (read as metres per second squared, or metres per second per second). It can be either positive, indicating an increase in velocity through time, or negative, which represents the object slowing down. Like velocity, it is a vectorial quantity, meaning it has a direction as well as a magnitude.

Displacement is also a vector, this time referring to the position of the object from its start point. It is independent of the path the object has travelled, for example if a ball is fired straight up into the air from the ground, reaches a height of 5m, and then drops back to the same point from which it was fired, the displacement would be equal to zero, despite having travelled a total distance of 10m.

Throughout A-level, you will likely encounter two variations of simple harmonic motion: a mass on a spring, and a simple pendulum. These both follow the same principle. Both systems start in an "equilibrium position" - this means that the forces acting on the system are balanced, and hence the system will not move. If the mass on the spring was stretched from its equilibrium position and then let go, the system would begin to oscillate due to the elastic restoring force. When there is positive displacement (the spring is stretched out), this restoring force attempts to contract the spring, and vice-versa when there is negative displacement. The greater the displacement of the mass, the greater the restoring force in the spring, and hence the greater the acceleration of the mass back to its equilibrium position. The relation between displacement and acceleration can be seen in the equation:

                                                                    a = -(2πf)2x

This makes it clear that the magnitude of the acceleration a is directly proportional to the displacement x as mentioned previously, and that the mass accelerates towards the equilibrium position.

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