Coverting Simple Harmonic Motion Equation to a Rotational Model

In summary, the conversation discusses using Simple Harmonic Motion in a Matlab/Simulink model to calculate the change in rotational angle of an object attached to a pivot point. The object is moved by a perpendicular force and can rotate up to 90 degrees in either direction. The person also mentions an article in an IEEE publication that may have relevant formulas for this situation.
  • #1
james6008
14
0
Hi

I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass.

A perpendicular force is applied to this object and it rotates around that pivot point (moving left and right only). The pendulum model considers the gravity while this is not affected by gravity at all.

I wanted to know if there is a way I can make use of Simple Harmonic Motion to calculate the change in rotational angle (from initial condition where it is 0 degrees) when a perpendicular force is applied to this object. The maximum it can move is 90 degrees on either direction.

How can I use the calculated acceleration & velocity from the model to represent this angular change?
 
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  • #2
Is your object the balance wheel of a mechanical watch?

I asked because what you described sounds quite similar to an article I read in an IEEE publication about whether a tourbillion escapement has a real impact on the accuracy and precision of a watch's movement. I believe there were some formulas in that article that may address what you seek. If so, let me know and I'll try to dig up that article.

All the best.
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which an object moves back and forth in a straight line, with a constant amplitude and a constant period.

2. How can the equation for SHM be converted to a rotational model?

The equation for SHM can be converted to a rotational model by using the relationship between linear and angular motion. This involves substituting the linear displacement, velocity, and acceleration with their corresponding angular values.

3. What are the key equations for converting SHM to a rotational model?

The key equations for converting SHM to a rotational model are:
- Displacement: θ = x/r
- Velocity: ω = v/r
- Acceleration: α = a/r

4. What are the applications of converting SHM to a rotational model?

Converting SHM to a rotational model can be useful in a variety of engineering and physics fields, such as designing rotating machinery, analyzing pendulum motion, and understanding the behavior of torsion springs.

5. Are there any limitations to converting SHM to a rotational model?

Yes, there are some limitations to converting SHM to a rotational model. This method is only applicable when the motion is circular or involves a rotational component. Additionally, it assumes that the object is moving with a constant radius, which may not always be the case in real-world situations.

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