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Let the force constant of the spring, i.e. the force to produce unit extension, be k. Consider the spring in equilibrium under a load m. If, now, the spring is pulled down a further down a further distance x, the extra restoring force called into play is, by Hooke’s Law, equal to kx. When the spring is released, the equation of motion is therefore
Where x represent the acceleration towards the equilibrium position
Hence the motion is simple harmonic and the periodic time T is
Thus, the graph of T2 against the straight line.
At first sight it would appear that this straight line ought to go through the origin, whereas the actual line obtained in the experiment does not. This is because the effective mass (mo) of the spring has been neglected and the above equation ought to be written
Spiral spring, stands and clamps, slotted masses and hanger, stop watch.
Plot a graph with values of T²/s² as ordinates against the corresponding values of m/kg
Slope from which l may be calculated
Since when T=0, the magnitude of m0 is equal to be the negative intercept OC on the load axis of the graph
The definition of spring constant is characteristic of a spring which is defined as the ratio of the force affecting the spring to the displacement caused by it. The value of spring constant that we can get from the calculation above is, k=24. The definition of effective mass is a quantity that is used to simplify band structures by constructing an analogy to the behaviour of a free particle with that mass. The value of effective mass can be determined from plotting graph where x-intercept is equal to the value of effective mass. The value of effective mass of the spring that we get from the graph is kg.
The value of spring constant, k=24. The value of effective mass of the spring, kg.
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