Tuesday, May 5, 2015

Bouncing Ball I

I like this sort of high school physics. Made me think what happens when the ball hits the surface (at y = 0). I've included a spring component to give an elastic bounce. When the ball is above the y = 0 plane, the only force acting is gravity and so, in this region,  the acceleration y'' equals g, where g is acceleration due to gravity (e.g. -10 m/s2 , minus since gravity is acting downwards). When the ball is below the plane, there is an additional elastic restoring force (acting upwards), equal to -ky (remembering y is negative below the plane!), so that y'' equals g - ky/m in this region.  

A damping force is readily included (representing a simple mechanical viscous damper (dashpot)), equal to -dy', where d is the damping coefficient (newton-seconds per meter), and y' the velocity. The initial height is specified by setting the initial condition of the second integrator (e.g. 5 volts for 5 m).


Initial height = 5 m; k = 100 N/m; d = 0.5 Ns/m.
Vertical axis 2 V per division, horizontal axis 0.2 seconds per division.



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