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1.2.3 Velocity LO (f)

From x = x_o sin ω t 

differentiating we get

where   v₀ = x₀ ω    is the maximum velocity

 
Variation with time of velocity  

In terms of x:

           
From mathematical identity     cos² ωt + sin² ωt = 1,

rearranging

cos² ωt       = 1 - sin² ωt

$$cos\omega t=\pm \sqrt{(1-<!--\; -\; -->si{n}^2\omega t)}$$
     
since

v       =  x₀ω cos ωt

where x₀ is the maximum displacement

$$v=\pm x_0\omega \sqrt{(1-<!--\; -\; -->si{n}^2\omega t)}$$    
 $$v=\pm x_0\omega \sqrt{(1-<!--\; -\; -->(\frac{x}{x_0}{)}^2)}$$$$$$

$$v=\pm \omega \sqrt{({x_0}^2-<!--\; -\; -->x^2)}$$

    

Variation with displacement of velocity

1.2.3.1 Model:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/72

 

Translations

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http://iwant2study.org/lookangejss/02_newtonianmechanics_8oscillations/ejss_model_SHM09/SHM09_Simulation.xhtml

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https://play.google.com/store/apps/details?id=com.ionicframework.shm09app611123&hl=en

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