The magnitude-squared of a complex number is the product of that number with its complex conjugate. The complex conjugate of a complex number is found by changing the sign of the imaginary part of the number: Z=a+bi⇒Z∗=a−bi⇒|Z|2=Z∗Z=(a−bi)(a+bi)=a2−(bi)2=a2+b2(6.2.4)

As with previous labs that involve extracting an answer from graphical methods, we will not be determining the uncertainty range for the final answer.  If you are not getting an answer witihin 5% of the actual mass of the magnet (you can measure this on the scale only after you have computed it!), then you have likely made one or more fixable mistakes.

height of its center of mass is what matters here.

Something we encountered in previous labs also comes up here. We are mapping the motion of the pendulum with the protractor behind it, so we need to minimize the effect of parallax in our view.  This is accomplished in the usual ways – keep the pendulum as close to the protractor as possible, and the camera as far away as possible (while still being able to see the result).

so that the top is prevented from going lower than the top of the post

The change in gravitational potential energy of the spring is determined by the distance that its center of mass rises. Some care must be taken to make sure you get this value correct, given that the spring is stretched at its lowest point and not stretched at its highest point.

measuring the minimum force we can apply to the object parallel to the surfaces that will make the object accelerate.