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Simple Harmonic Motion Pre

Simple Harmonic Motion Pre - can also be derived from these...

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Matt Darling Getts Section 3 Simple Harmonic Motion Pre-Lab This lab is designed to explore simple harmonic motion. Simple harmonic motion is defined as periodic motion that is occurring in a sinusoidal manner. Periodic motion is any motion that occurs in a regular way. Examples include pendulums and orbits. Simple harmonic oscillators include pendulums if the degree from equilibrium is small and a mass on a spring. The force required to stretch a spring is F=-KX. This is Hooke’s law where f is force k is the spring constant and x is the distance from equilibrium. The negative shows that the force goes opposite of displacement. One can’t combine newton’s second law without differential equations because acceleration is not constant in a spring however the equation gained from it can still be helpful. X(t) = Asin(sqrt(k/m)t+ o where A is amplitude, k is spring constant, m is mass, and o is phase. Angular frequency = sqrt(k/m) or ω which = 2pi/T where T is period. Velocity and acceleration
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Unformatted text preview: can also be derived from these equations. V(T) = Aωcos(ωt+0) and a(t) = -Aω^2sin(ωt+o). The energy of the system can also be analyzed since the energy of a spring is ½ kx^2 and kinetic energy is ½ mv^2. This gives Etotal = KE + PE. When expanded and simplified this gives E=1/2kA^2 = constant. So the total energy of a system in simple harmonic motion never changes. In the first part of the experiment the spring constant k will be measured using a force sensor. This is done by hanging a mass of known weight from the system and tracking it with DataStudio and finding k from the graph. The next part of the lab deals with the measurement of period. Find T using DataStudio and smart tool then determine angular velocity. Compare it to the calculated value and determine error. Input these values to view the conservation of energy on the graph. Check to see if the calculated values for total energy match and see if energy is indeed conserved in the system....
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