A uniform rod of mass m and length L is pivoted about an axle through one end. T

Question

A uniform rod of mass m and length L is pivoted about an axle through one end. The other end is attached to a horizontal massless spring of spring constant k. The spring is neither stretched nor compressed when the rod hangs straight down. The bottom end of the rod is pulled to the right and released. The system oscillates in simple harmonic motion. You can assume the rod's angle from the vertical is always small. Starting with Newton's second law for rotation, write a differential equation for the position theta of the rod as a function of time. i.e. write the equation of motion for the system. (Hint: Do not neglect the gravitational force.) Assume theta = theta max at time t = 0. Write the solution to your differential equation. In other words, determine an equation for the position theta of the rod as a function of time t. From the solution to your differential equation, determine the angular frequency co and period T of oscillation of the rod.

Explanation / Answer

(a).


Let ? is the rod

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