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 suffer the spring) and y is positive in the upward direction.
99. Use equation (4) to answer the following questions.
a. Find the second derivative
b. Verify that
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage