Suppose an object of mass m is attached to the end of a spring hanging from the
Question:
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
here 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.
Use equation (2) to answer the following questions.
a. Find the second derivative d2y/dt2 .
b. Verify that d2y/dt2 = -(k/m)y.
Step by Step Answer:
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett