On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

<div>A comparison between the approximate analytical solution (<a href="https://static.hindawi.com/articles/mpe/volume-2021/6678102/figures/#EEq50">50</a>) (dotted curve) and the RK4 numerical solution (dashed curve) is investigated for RLC series circuits parameters <span class="nowrap"><svg height="11.5564pt" id="M172" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 57.0051 11.5564" width="57.0051pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 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Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications 