Question

solve questions 4,5,6 please. thanks

Show all your work and final answers on these pages. Attach the requested graphs. Background for Laboratory Experiment 6 In Experiment 6, you will study the dynamic behavior of an electroacoustic system (or speaker). The background for this Pre-Lab is in Section 6.7.5 in the textbook. A physical model of the electroacoustic system is shown in the figure below. Speaker enclosure Magnet The motion of the center of the speaker cone is x. The motion is reference to an equilibrium position Sound waves The coil is connected to the center of the speaker cone so that it moves a distance x when the center of the cone moves a distance x. Coil Diaphragm 1) 3 pts) Derive a transfer function model for the speaker that relates the Laplace Transform of the output displacement X(s) to the Laplace Transform of input voltage V(s), assuming all initial conditions are equal to zero. Show all your work on the following page, starting with Newton's Law for the diaphragm and connected inertia, and Kirchhoff's voltage law for the circuit. © Karl N. Reid 2) pj Set L 0. Rewrite the transfer function as the reduced model below. X (s) V (s) 3) (1 py Write the transfer function in the form below. (Keep in terms of m, k, KnKb, R, & c) Show your work. x(s) V (s) 4) I1 pty Assume that the speaker parameters are as follows: k 4 x 105 N/m K 13 V. m = 0.002 kg K 16 N/A R 5.91 Ω (L 0 H) nl 4.4 N s/m termine numerical values for the undamped natural frequency on and the damping ratio ζ. 5) t po The speaker is driven by a step function in the input voltage of v(t) 5v. Determine an analytical expression for the response of x vs. time using the Laplace Transform method (Pair 23). Show all your work x(t) = 6) 13 pts) Plot x vs. time and attach your graph to the end of this Pre Lab. Include a title, labels on the axes, & units on the graph) 4

Answer 1

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