Vibrations of a spring Suppose an object of mass m is attached to the end of a spring hanging from the ceiling. The mass is at its equilibrium position y = 0 when the mass hangs at rest. Suppose you push the mass to a position y0 units above its equilibrium position and release it. As the mass oscillates up and down (neglecting any friction in the system), the position y of the mass after t seconds is
where k > 0 is a constant measuring the stiffness of the spring (the larger the value of k, the stiffer the spring) and y is positive in the upward direction.
100. Use equation (4) to answer the following questions.
a. The period T is the time required by the mass to complete one oscillation. Show that
b. Assume k is constant and calculate
c. Give a physical explanation of why
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CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
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