The aim of this first experiment is to examine simple harmonic motion exhibited a mass on a spring. Using data recorded in doing this, the spring constant for each spring can be calculated along with a value for gravity. In the first part of this experiment, the relationship between the period of the oscillations of the spring and the mass of the spring is observed. The period of oscillation of mass on a spiral spring depends on the mass on the spring and the spring constant of the spring.
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This is given by: Where m is the mass on the spring and k is the spring constant of the spring. Since the period can be observed, and the mass on the spring is known, this part of the experiment is concerned with calculating k, the spring constant for each of the springs used. The spring constant is different for every spring, and is defined as the mass needed to produce a unit extension of the spring (ref. 6).
This is calculated by placing differing masses on the spring, extending the spring a certain distance from its equilibrium position each time and timing the time for 10 oscillations of the spring to occur. This is done by using an analogue stopwatch and a ruler to ensure that the distance extended from the equilibrium position was the same each time. The graph of period squared against mass can then be plotted.
From this, the value for the spring constant, k, of each spring can be calculated by comparing the equation of the best fit line of the graph to the squared version of the equation above,. The second part of this experiment is concerned with Hooke’s law, which states that the extension of a spring is directly proportional to the mass applied to it. Mathematically, this is stated as: Where x is the extension of the spring in metres, k is the spring constant of the spring measured in Nm-1 and F is the restoring force, measured in Newtons.
This value is negative because the force always acts against the direction of the extension, for example if the extension of the spring is downwards, then the restoring force is the force acting upwards on the mass. When a mass is placed on a spring, it begins to oscillate, until it comes to rest. When the mass comes to rest, the two forces acting on it (the restoring force and gravitational force,) are balanced, ie: So it can be said that: , When a mass, m, is at rest on a spring with spring constant k, extension x from the equilibrium position, with g being the acceleration due to gravity of 9. 1Nkg-1 .
In this experiment, the spring is loaded with different masses of known values and the extension of the spring from the equilibrium position when there is no mass on the spring is recorded. Then a graph of extension against mass can be created from this data. The equation of the best fit line of this data can now be compared to and a value for the Earth’s gravitational field strength can now be calculated using this data and the value for the spring constant calculated in the first part of this experiment.