In the diagram below, the center of a disk of mass M is attached to a spring of

Question

In the diagram below, the center of a disk of mass M is attached to a spring of spring constant k. The other end of the spring is connected to a fixed wall. When the spring is at its resting length, the center of mass of the disk is at x = 0. Then the disk is rolled a distance A from the equilibrium position and released, allowing it to roll back and forth under the influence of the spring. (a) Starting from Newton’s second law for rotation, show that the x-coordinate of disk’s center of mass obeys an equation of the form

Explanation / Answer

Force , F = -K*x , where k IS SPRING CONSTANT

F = m*a

m*d2Xcm/dt^2 = -K*Xcm

d2Xcm/dt^2 =  -K/m * Xcm

d2Xcm/dt^2 = - omega^2 * Xcm

where omega^2 = K/m.

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