Simpleharmonicmotion
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This document discusses simple harmonic motion and provides useful formulas. It explains that the period of a simple pendulum is calculated as T = 2π√l/g, where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. For an elastic spring undergoing simple harmonic motion, the total energy is calculated as the kinetic energy (1/2mv^2) plus the potential energy (1/2kx^2), where k is the spring constant. The document also states that the total energy is equal to the maximum potential energy when the kinetic energy is zero, and equal to the maximum kinetic energy when the potential energy is zero.
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Simpleharmonicmotion
- 1. PHYSICS SIMPLE HARMONIC MOTION Short revision series
- 2. s θ PP’ K.E = 0 V = 0 P.E = max = mgh P.E = 0 V = max K.E = max =1/2 mv2 h
- 3. Useful formulae Period of a simple pendulum T = 2π √l/g l = lenght of simple pendulum g = acceleration due to gravity T = period Angular velocity ω = θ/t Θ = angle turned by body t = time takken Linear velocity v = rω
- 4. Acceleration of SHM Angular acceleration is the rate of change of angular velocity with time α = a/r a = αr Frequency – number of complete revolutions per min f = 1/T
- 5. Energy of SHM shm θ PP’ K.E = 0 V = 0 P.E = max = mgh P.E = 0 V = max K.E = max =1/2 mv2 h
- 6. In an elastic spring, F =kx; F being the force used to stretch the spring by a distance, and k = force constant Work done = ½ force x displacement x Kx/2 x X = ½ kx Therefore energy in the spring = ½ kx2 The maximum P.E = ½ kx2
- 7. K.E at any instant = ½ mv2 At position of maximum displacement v = 0 therefore K.E = 0 At that point the total energy = K.E + P.E = 0 + ½ kx2 Total energy = ½ kx2
- 8. At equilibrum when K.E is max, P.E = 0 Total energy will be = K.E + P.E = ½ mv2 + 0 = ½ mv2 But at any other positions besides position of maximum displacement and position of equilibrum total energy = KE + PE = ½ mv2 + ½ kx2
- 9. At position P and P’ which is when there is maximum displacement TE = PE + 0 = mgh θ PP’ K.E = 0 V = 0 P.E = max = mgh P.E = 0 V = max K.E = max =1/2 mv2 h
- 10. End