# Pendulum acceleration

I'm trying to do an experiment about earthquake... I used a pendulum and an "angle meter" (is that what it's called?) to measure the maximum angular displacement of the ball, thus define the strength of the earthquake. I measured the height the ball goes (enable me to find potential energy), and reason the bigger the angle, the stronger the earthquake (common sense, I know, but my teacher wants some calculation). But now my teacher want me to use tangential and radial acceleration to calculate the earthquake force...I try to read, but it seems strange somehow...I can't think of a way to calculate this...

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rock.freak667
Homework Helper
Well I guess you'd want to start by drawing the pendulum at an arbitrary angle,$\theta$ and then draw all of the forces acting on it.

I'm not sure how you intend for your measurement device to work. Are you thinking that it will measure horizontal accelerations, i.e. what you might experience at the top of a tall building that sways side-to-side in response to the earthquake?

If the earthquake produces mainly vertical displacements - and thus vertical accelerations - then I'm not sure how your pendulum would measure this.

Assuming you are measuring only the horizontal motion, then yes it makes sense that the maximum angular displacement would be related to the strength of the earthquake, but I think your teacher wants to to quantify this somehow. For example, if you measure that your pendulum has swung to 30 degrees from vertical, what does that indicate about the earthquake? The horizontal force exerted on the pendulum? The energy required to move it that far?

You need to be able to translate your angle to some quantity that relates directly to the strength of the earthquake.

You might consider a simpler version, namely a mass connected to a spring, such that it is able to move in a horizontal direction. Since it's a one-dimensional problem, it's a bit easier, and then once you have it solved you can then extend it to the case of a mass suspended by three perpendicular springs (in the x, y, and z directions) and thus measure displacements in all directions. This is the basic design of an accelerometer.

Thank you very much! I think I have no clue...Actually he's asking me to help a 9th grade student with his project today (in the last minute...great...). I've never seen the actual thing. But I think I'm measuring, as you say, horizontal earthquake. Our lab lost the accelerometer...
I would say that the potential energy thing is the easiest thing for a 9th grader now...(he has 2 more days, he can't learn angular stuff that fast...I think). I say that the KE from the earthquake move the ball in the pendulum to a height (because it is hung by a string). Using the angle, I can calculate the vertical displacement of the ball, and this is how the angle related to the strength of the earthquake... Do you think this is enough...or is there any flaws in what I'm saying...?
My teacher is worrying that the judges will ask him about tangential and radial acceleration, but I think, at this point, (and at his level), the judges will not ask such a thing...
Thank you all again!