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# lecture33 - Harmonic Motion(II(Serway 15.2 15.3 Mass and...

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Physics 1D03 - Lecture 33 1 Harmonic Motion ( II ) (Serway 15.2, 15.3) Mass and Spring Energy in SHM

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Physics 1D03 - Lecture 33 2 Velocity and Acceleration 2 MAX MAX 2 2 : Note ) cos( ) ( ) sin( ) ( ) cos( ) ( ϖ ϖ ϖ ϕ ϖ ϖ ϕ ϖ ϖ ϕ ϖ A a A v x t A dt dv t a t A dt dx t v t A t x = = - = + - = = + - = = + = a ( t ) = - ϖ 2 x ( t )
Physics 1D03 - Lecture 33 3 Energy in SHM M Look again at the block & spring ( 29 ( 29 energy) mechanical (total constant a ) ( cos ) ( sin ) ( cos ) ( sin ! ) ( cos ) ( sin 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 1 2 2 1 = = + + + = + + + = + = + = = + = = kA t t kA t k t m A U K k t kA kx U t A m mv K φ ϖ φ ϖ φ ϖ φ ϖ ϖ φ ϖ φ ϖ ϖ We could also write E = K+U = ½ m(v max ) 2

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Physics 1D03 - Lecture 33 4 Question : Suppose U= ½ kA 2 at t = 0, and T=1 sec. When is U = K during the cycle? (i.e. when do their curves cross?) radians in Put does When 4 7 4 5 4 3 4 2 2 2 2 1 2 2 2 1 2 2 1 2 2 1 , , , 315 , 225 , 135 , 45 ) sin( ) cos( ) ( sin ) ( cos ) sin( ), cos( ? π π π π = ° ° ° ° = ϖ ϖ ± = ϖ ϖ ϖ = ϖ ϖ ϖ - = ϖ = = t t t t A m t kA t A v t A x mv kx sec sec, sec, sec, 2 sec 1 8 7 8 5 8 3 8 1 at and rad if So = = π = ϖ = ϖ = t K U T T
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lecture33 - Harmonic Motion(II(Serway 15.2 15.3 Mass and...

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