A small sphere B of mass m is released from rest at the position shown and oscillates freely in a vertical plane, first around of O and then around peg A after the string enters in contact with the plug. Determine the tension in the string a) just before the string makes contact with the peg, b) just after the string makes contact with the peg.

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Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.8 × 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. a)What effective force constant should the springs have to make them oscillate with a period of 1.4 s in N/m? b)What energy is stored in the springs for a 1.8 m displacement from equilibrium in J?

a top view of an object of mass M connected between two stretched rubber bands of length L. The object rests on a frictionless surface. At equilibrium, the tension in each rubber band is T. Find an expression for the frequency of oscillations perpendicular to the rubber bands. Assume the amplitude is sufficiently small that the magnitude of the tension in the rubber bands is essentially unchanged as the mass oscillates.