Simple Harmonic Motion | Derivations of x,v,a

 

Below topics have been covered in this lecture: Conditions for Linear SHM, Simple Harmonic Motion Key Terms, Mean Position, Amplitude in SHM, Time Period and Frequency of SHM, Phase in SHM, Phase Difference, Simple Harmonic Motion Equation and its Solution, Solutions of Differential Equations of SHM, Quantitative Analysis of SHM, Velocity of a particle executing Simple Harmonic Motion, Kinetic Energy of a Particle in SHM, SHM as a Projection of Circular Motion

 

 x=displacement from mean positions, v=veleocity at position x, a=acceleration at position x, ϕ- initial phase angle, w=angular frequency, k=spring constant, A=amplitude 

 

TIMESTAMP 00:00 overview (x,v,a, KE,PE, TE) 03:58 k-Spring Constant 05:06 equations overview 05:53 w,T,f discussion 11:52 how to study SHM 13:15 definition of SHM 18:47 derivation starts 23:45 Mean and Extreme values 27:45 v^2=w^2(a^2-x^2) 33:14 x=Asin(ωt+ϕ) calculations 35:00 ϕ discussion 47:14 v=Awcos(wt+ϕ) calculations 48:30 a=-Aw^2sin(ωt+ϕ) calculations 49:10 T calculations 

 

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