Answer to Question #271611 in Physics for jay

Question #271611

If a simple harmonic oscillator has velocity function of:

v                =      100πAsin(100πt – 0.75π)   Find:

         i) an expression for displacement, x.    

         ii) an expression for acceleration, a. 


1
Expert's answer
2021-11-29T11:45:10-0500

Given:

"v =100\u03c0A\\sin(100\u03c0t \u2013 0.75\u03c0) "


(i) the displacement is related with velocity by formula

"x=\\int vdt\\\\=100\u03c0A\\int\\sin(100\u03c0t \u2013 0.75\u03c0)\\\\=-A\\cos(100\u03c0t \u2013 0.75\u03c0)"

(ii) the acceleration

"a=\\frac{dv}{dt}\\\\\n=(100\u03c0A\\sin(100\u03c0t \u2013 0.75\u03c0) )'\\\\\n=100^2\\pi^2A\\cos(100\u03c0t \u2013 0.75\u03c0)\n"


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