El gráfico de la función cruce el eje T con f = 0
o sea hay que resolver la ecuación:
$$\left(2 \sin{\left(10 \sqrt{6} t \right)} + 2 \cos{\left(10 \sqrt{6} t \right)}\right) e^{- 20 t} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje T:
Solución analítica$$t_{1} = - \frac{\sqrt{6} \pi}{240}$$
Solución numérica$$t_{1} = 24.4646380103376$$
$$t_{2} = 30.2361122460659$$
$$t_{3} = 92.3115240259002$$
$$t_{4} = 0.224446220278326$$
$$t_{5} = 72.3037466753751$$
$$t_{6} = 20.2322235708034$$
$$t_{7} = 84.2314600958804$$
$$t_{8} = 28.3122875008231$$
$$t_{9} = 76.2796511488769$$
$$t_{10} = 80.2555556223787$$
$$t_{11} = 18.3083988255606$$
$$t_{12} = 78.3317308771359$$
$$t_{13} = 48.3200648513482$$
$$t_{14} = 12.2804146237998$$
$$t_{15} = 10.2283348955409$$
$$t_{16} = 36.2640964478267$$
$$t_{17} = 2.27652594853731$$
$$t_{18} = 34.7250366516325$$
$$t_{19} = 6.25243042203909$$
$$t_{20} = 82.3076353506376$$
$$t_{21} = 70.2516669471161$$
$$t_{22} = 16.2563190973016$$
$$t_{23} = 100.263332972904$$
$$t_{24} = 74.2275714206179$$
$$t_{25} = 14.3324943520588$$
$$t_{26} = 38.3161761760857$$
$$t_{27} = 98.6585242791582$$
$$t_{28} = 32.2881919743249$$
$$t_{29} = 8.30451015029807$$
$$t_{30} = 44.2514987830153$$
$$t_{31} = 86.2835398241394$$
$$t_{32} = 26.2602077725642$$
$$t_{33} = 22.2843032990624$$
$$t_{34} = 96.2874284994019$$
$$t_{35} = 90.2594442976412$$
$$t_{36} = 68.3278422018733$$
$$t_{37} = 62.2998580001126$$
$$t_{38} = 4.32860567679629$$
$$t_{39} = 50.243889596591$$
$$t_{40} = 42.2920806495875$$
$$t_{41} = 88.4638745354146$$
$$t_{42} = 60.2477782718536$$
$$t_{43} = 64.2236827453553$$
$$t_{44} = 94.235348771143$$
$$t_{45} = 56.2718737983518$$
$$t_{46} = 52.29596932485$$
$$t_{47} = 54.348049053109$$
$$t_{48} = 66.2757624736143$$
$$t_{49} = 46.2679851230892$$
$$t_{50} = 58.3239535266108$$
$$t_{51} = 40.2400009213285$$