An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation

<div>The value of <svg height="15.0704pt" id="M53" style="vertical-align:-5.3645pt" version="1.1" viewbox="-0.0498162 -9.7059 15.4485 15.0704" width="15.4485pt" 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="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.304,3.132)"><path d="M518 50L491 51C452 54 444 60 444 110V444C429 441 405 437 377 434C348 430 314 427 287 426V403L323 397C356 392 365 386 365 333V99C331 66 293 51 257 51C212 51 169 75 169 164V299C169 366 169 413 172 444C156 441 128 437 101 433C75 430 50 427 29 426V403L57 397C82 391 90 386 90 333V137C90 29 147 -12 214 -12C241 -12 262 -4 291 13S342 48 365 65V-6L371 -12C390 -7 415 1 441 8C468 15 496 21 518 24V50Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.026,3.132)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g></svg> and <svg height="12.9787pt" id="M54" style="vertical-align:-3.272799pt" version="1.1" viewbox="-0.0498162 -9.7059 26.5373 12.9787" width="26.5373pt" 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="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.304,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.109,3.132)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.604,3.132)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.864,3.132)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z"></path></g></svg> with the variety of ∆<i>t</i>. 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Shock and Vibration

fig5

Figure 5

Figure 5: An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation 