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AP Physics C: Mechanics
7.5 Simple and Physical Pendulums
7.2 Frequency and Period of SHM
2.8 Spring Forces
Multi-Unit
AdvancedMCQMathematicalConceptual13.7k
A schematic diagram showing a vertical uniform rod of length \(L\) and mass \(M\) pivoted at its lower end by a small circular hinge anchored to a horizontal surface. A horizontal ideal spring with force constant \(k\) is attached to the midpoint of the rod, a distance \(L/2\) above the hinge, and extends horizontally to the left to anchor against a fixed vertical wall with hatching. A vertical dashed line indicates the equilibrium position of the rod. A second, identical rod is drawn tilted slightly to the right by an angle \(\theta\) relative to the vertical dashed line, with an arc labeled \(\theta\) between them near the bottom pivot. An arrow labeled \(g\) points vertically downward to indicate gravitational acceleration. No other labels, lines, text, or axes appear.
A uniform rod pivoted at its base and supported by a horizontal spring at its midpoint.
A uniform rod of mass \(M\) and length \(L\) is attached to a frictionless pivot at its base so that it can rotate freely in a vertical plane.

A horizontal ideal spring of force constant \(k\) is connected between a fixed vertical wall and the midpoint of the rod, as shown.

The rod is in equilibrium in the vertical position where the spring is unstretched.

Assuming \(k > \dfrac{2Mg}{L}\), what is the angular frequency of small-amplitude oscillations of the rod about this equilibrium position?

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