A uniform heavy spring of mass m, and stiffness k is attached at one end to...

  

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A uniform heavy spring of mass m, and stiffness k is attached at one end to a mass m that is free to roll on a frictionless horizontal plane, and the other end is fixed. A schematic diagram of this system is shown in Fig. 2. 32. Assume that the velocity distribution along the spring is given by v, (x)=vsin 21 where / is the unstretched length of the spring, v is the velocity of the connected mass, a is the distance of a point along the spring from the fixed end. Determine an equivalent lumped mass of this system to represent the inertia effects of the spring. diw ndi e bmaho h nin sdraalusis In sd Fig. 2. 32 A heavy spring connected to a rolling muss A uniform heavy spring of mass m, and stiffness k is attached at one end to a mass m that is free to roll on a frictionless horizontal plane, and the other end is fixed. A schematic diagram of this system is shown in Fig. 2. 32. Assume that the velocity distribution along the spring is given by v, (x)=vsin 21 where / is the unstretched length of the spring, v is the velocity of the connected mass, a is the distance of a point along the spring from the fixed end. Determine an equivalent lumped mass of this system to represent the inertia effects of the spring. diw ndi e bmaho h nin sdraalusis In sd Fig. 2. 32 A heavy spring connected to a rolling muss