A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will

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become T/$\sqrt$(2) Time period \left( T \right) is given by, T = 2$\pi$$\sqrt$(m/k) where m is the mass, and k is spring constant. When the spring is divided into two parts, the new spring constant k1 is given as, k1 =2k New time period T1 : T1 = 2$\pi$$\sqrt$(m/2k) = 1/$\sqrt$(2)2$\pi$$\sqrt$(m/k) = 1/$\sqrt$(2)T

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