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Unformatted text preview: EXPERIMENT Hooke’s Law and SIMPLE HARMONIC MOTION Introduction: Any elastic material tends to return back to its original shape after experiencing deformation. This means that elasticity implies a restoring force. For many elastic substances the deformation is directly proportional to the restoring force, a relationship that was first demonstrated by Robert Hooke (1635-1703). For a mass-spring system, the elastic force acting on the mass has the form: F = – k x (1) where x is the linear displacement, or the amount of stretching, of the spring ( = x f – x i ). The stretched and unstretched positions, respectively, are x f and x i . The constant of proportionality k is characteristic of the spring and is called the “force constant”, “spring constant”, or “stiffness constant”. It is a relative indication of the “stiffness” of the spring. For experimental convenience we may neglect the minus sign in the above mentioned equation. When the suspended mass is displaced from the equilibrium position the system starts to oscillate. The “periodic motion” is the repeated motion of an object in equal time periods. When the motion obeys Hooke’s law, it is called “Simple Harmonic Motion” (SHM). “Simple” because the restoring force has the simplest form and “harmonic” because the motion can be described by “harmonic functions” (sines and cosines). For a mass oscillating on a spring, please review your textbook. It can be shown that: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = T t A y π 2 cos (2) where y = y f – y i is the vertical displacement, T is the “period of oscillation”, and A the “amplitude”, i.e. the maximum displacement of the mass. The period of oscillation is given by: “amplitude”, i....
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