iMecaProf and Pendulum


 

Pendulum:  see http://en.wikipedia.org/wiki/Pendulum





m= mg + T


= R d2θ/dt2  n - R [dθ/dt]2  u


Length R is known




In iPhone frame, one has:


a = ax.iphone + ay.jphone + az.kphone 


When the iPhone is used as a mass m and well oriented, this becomes : 


u = jphone and n = kphone


and therefore : 



From either from the magnetometer (by mind all the magnets and the metallic pieces in neighborhood...) or from the gyroscope (mind drift), pitch, roll and yawl are known. 



Therefore from iPhone embedded sensors, one gets in real time : 




Key equations when studying the pendulum are:

    • From Newton second law:  m= mg + T  gives : 


R.d2θ/dt2 + g.sin[θ] = 0


    • Conservation of mechanical energy: 


Em = 1/2 m R 2 [dθ/dt]+ m.g.R.{1-cos[θ]}


In red are the measured quantities by iPhone sensors and send in real time to the a PC to either shown on screen or saved for post-treatment.


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