How to solve Pendulum
Asimplependulumofmassmhasanaccelerometerplacedinsideit.Itcanread acceleration values in the x,y, and z axis in its frame of reference. What values does
the accelerometer read when the pendulum is at the highest point and the lowest point?
Accepted answer
Assuming zero drag from air resistance, a perfect pivot bearing, and the accelerometers at the CG of the pendulum assembly…
Since the pendulum is only constrained in the Z-axis, the only reading will be in the Z-axis. X and Y will read zero acceleration at all pendulum positions.
When the pendulum is at its lowest point in the vertical position (theta=0), the Z-axis accelerometer will read more than 1 G. It will be the sum of gravity (1G) and the centripetal acceleration of the pendulum rotating about the pivot. The actual centripetal acceleration can be calculated using the theta angle at the highest point of the swing. I don’t remember the exact equation but it’s easy to find on the web. The centripetal acceleration is irrelevant of the mass and the length of the pendulum.
When the pendulum is at its highest point, the Z-axis accelerometer will read less than 1 G. Since it is briefly motionless at that instant there is no centripetal force. The accelerometer will read 1G times the cosine of theta.
1 Other answer
Hi @Kamran Yunus
To complement what Bob said, I suggest you "learn by experimenting". That's easy with CADD-CAE: you just have to draw and simulate the kinematics and dynamics.
I bring you a schematic pendulum drawn in SolidWorks 2017 mounted in an assembly to be able to simulate it with Motion. One of the great advantages of Motion is that it allows you to graph positions, velocities, accelerations, forces, etc.
It's a relaxed way to learn (simpler than analyzing math equations, although this too will be important to do at some point, when you've already intuitively understood the problem).
This "virtual laboratory" will allow you to test and answer questions in seconds, such as: will the movement of the pendulum change if its mass is greater? will its frequency change? what happens if i make it longer or shorter? ... and many etc etc. that make it easier and more interesting to study these phenomena.
Best regards!
