Question

please solve question 5-6 and clearly mark correct answers and steps. thanks

MAE 3724 Systems Analysis Pre-Lab for Experiment 6 Electroacoustic System /Speaker Complete this Pre-Lab BEFORE you come to the laboratory. The Lab Instructor will answer questions and provide feedback when you come to the laboratory to do the experiment. 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 χ. 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) 13 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. starting with Newton's Law for the diaphragm and connected inertia, and Kirchhoffs voltage law for the circuit. VCS O Karl N. Reid 5) 1t 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) 3 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)

Answer 1

Pom newton's laus di dt df fic eft speaketmo Conss equah sive ry unei m1s3.tatme)s (kl+ c R4 krea)

X(s) ves) m R x(s) M R

1LS to3

xG) 1,360.25 3000 :C