# Mass on a Spring

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Experimental Design Focus question: What is the relationship between strain and time? Hypothesis: The more springs added, the mass will vibrate quicker. The more mass added, the longer it will take to vibrate. Vice versa, the more springs taken away, the longer the mass will take to vibrate. The more mass taken away, the quicker it will vibrate. Theory: Oscillation is a way of returning a system to its equilibrium position, the stable position where there is no net force acting on it. Once a system is thrown off balance, it does not return to is original state; it oscillates back and forth about the equilibrium position. The movement of an oscillating body is called harmonic motion. The oscillating motion of a spring is caused by the stretching or compression of it. As the spring is stretched then released, it will exert a force, pushing back the mass until it reaches its amplitude of its motion. The amplitude can then be used in Hooke’s Law in order to understand the manner in which the spring exerts a force on the mass attached to it which is F=kx; ‘x’ being the equilibrium point, ‘k’ being the spring constant and ‘F’ being the restoring force. Hooke’s law states that the further the spring is stretched from its equilibrium point, the greater the force the spring will exert towards its equilibrium point. Because ‘F’ and ‘x’ are directly proportional, a graph of ‘F’ vs ‘x’ is a line with slope ‘k’ A mass on a spring is a simple harmonic oscillator which is an object that oscillates the equilibrium point and experiences a restoring force proportional to the object’s displacement. The time it takes for a spring to complete an oscillation is called the period of oscillation, ‘T’. The period of oscillation of a simple harmonic oscillator that is described by Hooke’s Law is: T=2π√(m/k). This formula shows that as the mass, ‘m’, increases and the spring