Solved: A system consists of a vertical spring with force

Chapter , Problem 76

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A system consists of a vertical spring with force constant k 5 1 250 N/m, length L 5 1.50 m, and object of mass m 5 5.00 kg attached to the end (Fig. P13.76). The object is placed at the level of the point of attachment with the spring unstretched, at position yi 5 L, and then it is released so that it swings like a pendulum. (a) Write Newtons second law symbolically for the system as the object passes through its lowest point. (Note that at the lowest point, r 5 L 2 yf .) (b) Write the conservation of energy equation symbolically, equating the total mechanical energies at the initial point and lowest point. (c) Find the coordinate position of the lowest point. (d) Will this pendulums period be greater or less than the period of a simple pendulum with the same mass m and length L? Explain.