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oscillation.ppt

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oscillation.ppt
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Chapter 15 Oscillations,Simple Harmonic Motion:,Any motion that repeats itself in equal intervals of time is called periodic motion.,T is called period. f=1/T is frequency.,amplitude angular frequency phase initial phase,the quantities about SHM,(1) period, frequency, and angular frequency,The period of the cosine function is,So the period of SHM is,angular frequency,(2) amplitude,at,(3) phase,initial phase,The initial phase can be determined by both the initial position and velocity.,Example 1: The motion function of a harmonic oscillator is . The initial position is and initial velocity is,Find the amplitude and initial phase.,Solution:,The phase difference between two SHMs,in phase,in opposition,The velocity and acceleration of SHM,Simple Harmonic Motion and Uniform Circular Motion,旋转矢量法,The projection of uniform circular motion is simple harmonic motion.,The Force Law for SHM,(1) Linear Simple Harmonic Oscillator (简谐振子),Hooke’s Law,Newton’s Second Law,where,The solution is,(2) The Simple Pendulum (单摆),when,then,Newton’s Second Law,where,(3) Other examples:,Torsion pendulum (扭摆),restoring torsion,Physical Pendulum (物质摆),,Prove: Any small oscillates around equilibrium point is simple harmonic oscillation.,Proof:,The potential energy,Exercise: two identical springs of spring constant k are attached to a block of mass m. What is the frequency of oscillation on the frictionless floor?,Energy in Simple Harmonic Motion,Kinetic energy:,Potential energy:,Mechanical energy:,K and U are also simple harmonic oscillations. They are in opposition. The period is T/2.,Average kinetic energy during a period,Average potential energy during a period,Example 2: A block of mass M, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k. A bullet of mass m and velocity v strikes and is embedded in the block. Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed o
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