Answer to Question #271611 in Physics for jay

Question

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. 

Answer 1

Given:

$v =100πA\sin(100πt – 0.75π)$

(i) the displacement is related with velocity by formula

$$x=\int vdt\\=100πA\int\sin(100πt – 0.75π)\\=-A\cos(100πt – 0.75π)$$

(ii) the acceleration

$$a=\frac{dv}{dt}\\ =(100πA\sin(100πt – 0.75π) )'\\ =100^2\pi^2A\cos(100πt – 0.75π)$$