## Tuesday, February 11, 2020

### Loaded Spring Oscillator, Hooke's Law Assignment

Loaded Spring Oscillator, Hooke's Law - Assignment Example The motion involves attachment of simple harmonic oscillator to the spring with the other end on the wall or any other rigid support system. The oscillatorÃ¢â‚¬â„¢s motion is repetitive at constant frequency hence periodic (Serway & Jewett, 2006 p 54). When the oscillator passes through the equilibrium its velocity is maximum and zero when passing through the extreme positions in its oscillation. The acceleration experienced by the oscillator is proportional to the negative of its displacement from the midpoint of its motion. A system in equilibrium and at rest has no net force acting on the mass. Displacement of the mass from equilibrium causes a restoring elastic force which obeys HookeÃ¢â‚¬â„¢s to be exerted by the spring. The restoring force F, is found by multiplying the spring constant K, to the displacement from equilibrium x; F=-Kx. The extension of a spring is directly proportional to the load applied to it. This is referred to the HookeÃ¢â‚¬â„¢s Law of elasticity. The mater ialÃ¢â‚¬â„¢s elastic limit is the maximum load that when exceeded the material will not be able to gain its original form. Therefore, HookeÃ¢â‚¬â„¢s Law do not apply on the material. The elastic limit varies among the materials. The materials following HookeÃ¢â‚¬â„¢s Law are known as Hookean materials or linear elastic materials. The materials regain their original form after deformation by the load on it. In the formulae used to determine HookeÃ¢â‚¬â„¢s Law a negative sign is added because the restoring force acts in an opposite direction of displacement. The formula was stated by Robert Hooke, a British physicist in the 17th century hence its name; HookeÃ¢â‚¬â„¢s Law. A spring of length L and cross-sectional area A, is considered a linear elastic material since its extension is linearly proportional to tits tensile stress by a constant. Materials such as rubber are regarded as non-linear or non-Hookean since the load is not proportional to the extension that occurs. The material c hanging least in extension when load is applied is regarded to have the greatest elastic force. Elasticity would be described in four ways; compression, flexure or bending, stretching or extension, torsion or twisting. Elasticity has two main kinds namely elasticity by volume and elasticity of form or shape. For example, elasticity of volume is mainly experienced by the gases and liquids. Elasticity of the two is considered perfect since when the load is applied or removed there is no lost of volume. Increase in temperature of the material would cause increased extension. Therefore, factors such as temperature are to be kept constant during the experiment to ensure the results are not misleading. The graph is expected to be as shown below: Figure 1 The springs are found to obey the HookeÃ¢â‚¬â„¢s law in combinations. Therefore the springs can be combined to cater for specific spring constant. For springs in series, the equivalent constant is equal to the following: 1/Keq = 1/K1 + 1/ K2 Therefore the equivalent spring constant is the reciprocal of the answer from above. If the springs are in parallel the equivalent spring constant is equal to the sum of the spring constants of the springs used. Keq = K1 + K2 The Apparatus The requirements for the experiment are the steel springs, tensile. Mass hangers with slotted masses, 100g. Retort stand base, rod, boss and clamp. Short length of stiff wire to combine springs in parallel. G-clamp if the retort stand base is