Chapter 13, Problem 80P

You’re a structural engineer working on a design for a steel beam, and you need to know its resonant frequency. The beam’s mass is 3750 kg. You test the beam by clamping one end and deflecting the other so it bends, and you determine the associated potential energy. The table below gives the results:

Beam deflection x (cm)	Potential energy U (J)
−4.54	164
−3.49	141
−2.62	71.9
−1.22	9.15
−0.448	0.162
0	0
0.730	4.13
1.29	16.3
2.13	34.0
3.39	115
4.70	225

Find a quantity which, when U is plotted against it, should give a straight line. Make your plot, determine the best-fit line, and use its slope to determine the resonant frequency of the beam.