Pendulum calculations 1

[jbknudsen]

Greetings to all.
I am trying to determine what the peak force or load (in lbs) is on a wire when a pendulum is at the apex of its swing. All of the calculations that I have found seem to deal with determining the time of a full cycle. I understand that I will need to have "time" and weight information in order to determine the load, I just cant find any formula for determining the peak load. Any suggestions are welcome.

Thanks,
Jay

 

[mloew]

jbknudsen,

Sounds like you need to draw the Free Body Diagram. The force will come from the mass x gravity and the instantaneous acceleration which you can figure out from the formulas you have. Acceleration is the second time derivative of position, remember.


Best regards,

Matthew Ian Loew

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[desertfox]

Hi jbknudsen

If you use an energy balance for the pendulum as follows
this should give you the peak force in the wire ie:-

kinetic energy = potential energy

1/2 * I * w^2 = m * g * h

now for a simple pendulum I=m * h^2, also assuming that the
pendulum is released from the horizontal plane and you are interested in the peak force in the wire when it reaches the vertical plane.

let h = the radius at which the mass acts for your pendulum

m = mass of rotating bob

g = gravity const

w = angular velocity

Now from the above you know I, g , m and h

so transpose formula to find w^2

therefore:- m *g * h / (0.5 * I) = w^2

now centrifugal force = m * w^2 * h

so once you have calculated the angular velocity squared you can find the centrifugal force.

Now the peak force in the wire would be the centrifugal force added to the static force of the pendulum bob

ie:- m * g + m * w^2 * h

hope this helps

regards

desertfox

 

[Cockroach]

Good Afternoon All:

The peak loading force is simply the centrifugal force induced by the angular momentum of the pendulum bob. In other words, the work-energy theorem will provide you with maximum velocity at the path nadir, which would be the greatest stress experienced by the pendulum.

Here's the bigger problem. If the arc of motion is greater than ten (10) degrees, standard approximation methods in typical textbooks DO NOT work. This is because you are assuming compounding errors associated with the differential equation of motion making the system linear, easier to solve using circular functions. In fact, the problem is an elliptic integral, closed form solution sets are found by numerical computation methods. Otherwise you need to generate or find an elliptical integral table and interpolate between values for the "complete case".

I recommend you use the work-energy model(s) to get velocity and then use the notion of centripedal force. This would be a standard first year engineering calculation.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[chicopee]

Desertfox's approach is good for small angular swings
and Cockroach's approach has good merits for large swings.