A uniform solid cylinder can roll without sliding on a horizontal surface as shown in the figure. The mass of cylinder is $10 kg$ and the spring constant for both the ideal springs is $300 N m^{- 1}$ . What is the angular frequency (in $rad s^{- 1}$ ) of small oscillations of the centre of the cylinder?

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The total energy of the system is E = 3 4 m v 2 + 5 2 k x 2 d E d x = 3 2 m a + 5 k x = 0 a = - 10 k 3 m x ⇒ ω = 10 k 3 m = 10 rad s - 1

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