Pulley-Pulley

Classical Mechanics Level 2

A pulley of mass m m , radius r r and moment of inertia I I about its axis hangs on a string connected to a spring of force constant k k as shown. Assume that the string does not slip over the pulley. Determine the time period of vertical oscillations.

Given: m = 2 K g , r = 1 m , I = 5 K g m 2 , k = 0.2 N m − 1 \boxed{m = 2 Kg, r = 1 m, I = 5 Kgm^{2}, k = 0.2 Nm^{-1}}

2 π 8 . 75 2\pi \sqrt8.75 2 π 7 . 25 2\pi \sqrt7.25 2 π 8 . 25 2\pi \sqrt8.25 2 π 6 . 75 2\pi \sqrt6.75

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