For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my''(t) + by'(t) + ky(t) = 0.
(a) Find the equation of motion for the vibrating spring with damping if m = 20 kg, b = 160 kg / sec, k = 500 kg / sec^2, y(0) = 0.3 m, and y'(0) = -0.9 m / sec.
(b) After how many seconds will the mass in part (a) first cross the equilibrium point?
(c) Find the frequency of oscillation for the spring system of part (a).
(d) The corresponding undamped system has a frequency of oscillation of approximately 0.796 cycles per second. What effect does the damping have on the frequency of oscillation? What other effects does it have on the solution?
(a) y(t) =
(b) The mass will first cross the equilibrium point after seconds.
(Round to three decimal places as needed.)
(c) The frequency of oscillation is cycles per second.
(Round to three decimal places as needed.)
(d) Complete the explanation of the effects of damping below.
The damping the frequency of oscillation. This because the force of friction will always be in the direction as the motion of the spring.
Additionally, the magnitude of the oscillations with time. This since friction is the system.