1. Solid cylinder of mass m is connected to the two springs of total stiffness k

Question

1.      Solid cylinder of mass m is connected to the two springs of total stiffness k as shown. Each of the springs is attached to a wall. Find the period of small oscillations of the cylinder assuming that it does not slide on the floor.

http://snag.gy/mpqcb.jpg

The diagram is above, listed as Problem 5.

Solid cylinder of mass m is connected to the two springs of total stiffness k as shown. Each of the springs is attached to a wall. Find the period of small oscillations of the cylinder assuming that it does not slide on the floor.

Explanation / Answer

angular acceleration: alpha

dynamic equation of motion are as follows-

(3*m*R^2 /2) * alpha = -k*(2*alpha*R)*2R           (1)    (applied about the contact point of cylinder and the floor)

--> alpha = - ( 8*k / 3*m) alpha

hence, T = 2*pi*sqrt(3m/8k)

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