Auniform rod of mass m and length L is pivoted about an axle throughone end. The

Question

Auniform rod of mass m and length L is pivoted about an axle throughone end. The other end is attached to a horizontal massless springof spring constant k. The spring is neither stretched norcompressed when the rod hangs straight down. The bottom end of therod is pulled to the right and released. The system oscillates insimple harmonic motion. You can assume the rod’s angle fromthe vertical is always small.

(a)Starting with Newton’s second law for rotation, write adifferential equation for the position of the rod as afunction of time. i.e. write the equation of motion for the system.(Hint: There are two restoring forces acting on therod.)

(b) From the solution to your differential equation,determine the angular frequency

oftherod. (Hint: sincos=1sin(2))2

(c)Determine the period of oscillation of the rod.

Explanation / Answer

displace the rod a small angle -k*L*=I*'' I=m*L2/3 =>=3k/m => period T=2m/3k

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