~OT: 3-axis outputs on a pendulum

Started by June 4, 2004
 I've been challenged to predict the outputs of a 3-axis accelerometer mounted on the end of a pendulum that swings through a cone, on Earth. Assuming the x and y axes are fixed north-south (i.e. the pendulum does not rotate in its suspension bearing), I expect that x and y will be sines in quadrature, the response to gravity's apparent motion. What of z, though? Will it be constant? And, will an unconstrained pendulum that is started in a conic swing continue to swing in a cone or will it settle to an arc, ala Foucault, anywhere but the Poles? Tom Tom Becker --... ...-- www.RighTime.com The RighTime Clock Company, Inc., Cape Coral, Florida USA +1239 540 5700
 Hi Tom, Indeed, the z-axis would be a constant reading as long as the motion stayed perfectly conical and did not decelerate. As soon as it starts to go into an "oval" cone, there will be a moment towards the outside of the ellipse where the pendulum will slow down compared to the rest of the motion, and thus the z-axis reading will change. The z-axis component will be a compound of g (towards the Earth's center) and the centrifugal/centripetal force in the pendulu's axis. Regarding the free-motion pendulum, over time it will set itself into a Focault-mode (so-to-speak), as the earth's motion does not provide the acceleration needed to keep two axis in motion. In a science museum in Barcelona we have a Focault pendulum, it's quite impressive as the suspension rod is some 30 meters high - it operates as a clock, slowly rotating the swing axis during the day and knocking down a small pole each hour. Regards, Mike ----- Original Message ----- From: "Tom Becker" <> To: <> Sent: Friday, June 04, 2004 5:42 PM Subject: [BasicX] ~OT: 3-axis outputs on a pendulum > I've been challenged to predict the outputs of a 3-axis accelerometer > mounted on the end of a pendulum that swings through a cone, on Earth. > Assuming the x and y axes are fixed north-south (i.e. the pendulum does > not rotate in its suspension bearing), I expect that x and y will be > sines in quadrature, the response to gravity's apparent motion. What of > z, though? Will it be constant? > > And, will an unconstrained pendulum that is started in a conic swing > continue to swing in a cone or will it settle to an arc, ala Foucault, > anywhere but the Poles? > Tom > > Tom Becker > --... ...-- > www.RighTime.com > The RighTime Clock Company, Inc., Cape Coral, Florida USA > +1239 540 5700 > Yahoo! Groups Links >
 Hmm, I don't know but I think the pendulum would slowly spiral inwards due to loss of energy (at the suspension point, and air resistance). In a Foucault pendulum the earth rotates under the pendulum's plane of vibration, which is sensibly fixed in inertial space (given no outside torques). So I would think that the pendulum would continue move with a conical motion of decreasing amplitude. If this is the case the z component would gradually grow and the amplitude of the x-y components would gradually decrease, but remain sinusoidal in quadrature. Rotating about the bearing point would have no bearing on the x,y,z motion, the pendulum body would just rotate about the line of the suspension cable (you can observe this with a small, hand held pendulum). John->Indeed, the z-axis would be a constant reading as long as the motion stayed >perfectly conical and did not decelerate. As soon as it starts to go into an >"oval" cone, there will be a moment towards the outside of the ellipse where >the pendulum will slow down compared to the rest of the motion, and thus the >z-axis reading will change. The z-axis component will be a compound of g >(towards the Earth's center) and the centrifugal/centripetal force in the >pendulu's axis. > >Regarding the free-motion pendulum, over time it will set itself into a >Focault-mode (so-to-speak), as the earth's motion does not provide the >acceleration needed to keep two axis in motion. In a science museum in >Barcelona we have a Focault pendulum, it's quite impressive as the >suspension rod is some 30 meters high - it operates as a clock, slowly >rotating the swing axis during the day and knocking down a small pole each >hour. > >Regards, > >Mike > >----- Original Message ----- >From: "Tom Becker" <> >To: <> >Sent: Friday, June 04, 2004 5:42 PM >Subject: [BasicX] ~OT: 3-axis outputs on a pendulum > > I've been challenged to predict the outputs of a 3-axis accelerometer > > mounted on the end of a pendulum that swings through a cone, on Earth. > > Assuming the x and y axes are fixed north-south (i.e. the pendulum does > > not rotate in its suspension bearing), I expect that x and y will be > > sines in quadrature, the response to gravity's apparent motion. What of > > z, though? Will it be constant? > > > > And, will an unconstrained pendulum that is started in a conic swing > > continue to swing in a cone or will it settle to an arc, ala Foucault, > > anywhere but the Poles? > > > > > > Tom > >
 > ... Rotating about the bearing point would have no bearing on the x,y,z motion... No, but it would change the accelerometer's x,y phases. If the pendulum rotates 360 degrees about its axis the accelerometer outputs will have advanced or retarded by the same angle. If one were to use the quadrature signals to count the conic swings, the count would be incorrect by four edges (one rotation) if the pendulum rotated one turn in its mount. Tom Tom Becker --... ...-- www.RighTime.com The RighTime Clock Company, Inc., Cape Coral, Florida USA +1239 540 5700