# Factors Affecting the Time Period for Oscillations in a Mass-spring System

When a mass is attached to the end of a spring the downward force the mass applies on the spring will cause the spring to extend. We know from Hooke?s law that the force exerted by the masses attached to the spring will be proportional to the amount the spring extends. F = kx When additional downward force is applied to the spring we can cause additional tension in the spring which, when released, causes the system to oscillate about a fixed equilibrium point. This is related to the law of conservation of energy. The stain energy in the spring is released as kinetic energy causing the mass to accelerate upwards. The acceleration due to gravity acting in the opposite direction is used as a restoring force which displaces the mass as far vertically as the initial amplitude applied to the system and the process continues. A formula that can be used to relate mass applied to a spring system and time period for oscillations of the system is T = 2Ï?âˆšM/k This tells us T2 is proportional to the mass To test this relationship an experiment will have to be performed where the time period for an oscillation of a spring system is related to the mass applied to the end of the spring.Variables that could affect T Mass applied to spring; Preliminary experiments should be performed to assess suitable sizes of masses and intervals between different masses used in the experiment. Spring constant; The spring constant will be useful to confirm the relationship. A simple force ? extension experiment should be performed to get an accurate value for k which can be compared to the value of k from the final experiment. Amplitude; The amplitude of the oscillations should be kept constant. Bear in mind the amplitude cannot be larger than the extension caused by the smallest mass applied to the spring as this would not allow the system to oscillate properly. Elastic limit of spring; If the spring has been extended past its elastic limit it will have become permanently deformed and will no longer obey Hooke?s law causing inaccuracies in the readings. Preliminary Experiment From preliminary experimentation I found that; Â? 0.03m is a suitable amplitude to give appropriate sized oscillations with minimal disruption at lower masses. Â? Due to a Â?0.01s error in the stopwatch it is sensible to only take readings of 1

Factors Affecting the Time Period for Oscillations in a Mass-spring System 7.5 of 10 on the basis of 3590 Review.