Manipulatedelastance[t0_, t1_, tdelay_, period_] := Module[{},

  Originalfunc =
   0.05 + Piecewise[{{3.95 (1 - Cos[2 Pi Mod[t, 1]/0.3])/2,
       Mod[t, 1] < 0.3}}];
  ToBeAddedfunction = 3.95 (1 - Cos[2 Pi Mod[t - tdelay, 1]/period])/2;
  Combinedfunction =
   0.05 + Piecewise[{{(((3.95)*(1 - Cos[2 Pi Mod[t, 1]/period])/2) +
          EVLtr2)/2, Mod[t, 1] < 0.3}}];



  EATtr =
   0.17 + Piecewise[{{0.73 (1 - Cos[2 Pi Mod[t - 0.9, 1]/0.1])/2,
       Mod[t, 1] > 0.9}}];
  EPATtr =
   0.2 + Piecewise[{{0.5 (1 - Cos[2 Pi Mod[t - 0.9, 1]/0.1])/2,
       Mod[t, 1] > 0.9}}];
  EPVLtr =
   0.08 + Piecewise[{{3.95/5 (1 - Cos[(2 Pi Mod[t, 1]/0.3)])/2,
       Mod[t, 1] < 0.3}}];



  {Plot[Originalfunc, {t, t0, t1}],
   Plot[{Originalfunc, ToBeAddedfunction, Combinedfunction}, {t, t0,
     t1}, PlotRange -> All,
    PlotLegends -> {"Originalfunc", "ToBeAddedfunction",
      "Combinedfunction"}],
   Plot[{Originalfunc, EATtr, EPATtr, EPVLtr, Combinedfunction}, {t,
     t0, t1}, PlotRange -> All,
    PlotLegends -> {"EVL", "EAT", "EPAT", "EPVL", "Enew"}]}]

Manipulate[
 Manipulatedelastance[t0, t1, tdelay, period], {{t0, 0}, 0,
  30}, {{t1, 2}, 0, 20}, {{tdelay, 0.7}, 0, 1}, {{period, 0.3}, 0, 1}]

OriginalFn[t_] := 0.05 + 3.95 Piecewise[{{1/2 (1 - Cos[2 Pi Mod[t, 1]/0.3]), Mod[t, 1] < 0.3}}]

ToBeAddedFn[t_, delay_, period_, amplitude_] := amplitude *
  Piecewise[{
    {1/2 (1 - Cos[2 Pi Mod[t - delay, 1]/period]), Mod[t - delay, 1] < period}
  }]

Manipulate[
  Row[{
    Plot[{OriginalFn[t], ToBeAddedFn[t, delay, period, amplitude]}, {t, 0, 0.4}, PlotRange -> {0.0, 4}, ImageSize -> 300],
    Plot[1/2 (OriginalFn[t] + ToBeAddedFn[t, delay, period, amplitude]), {t, 0, 0.4}, PlotRange -> All, ImageSize -> 300]
  }],
  {{period, 0.2}, 0.015, 0.3},
  {{delay, 0.003}, 0, 0.3 - period},
  {{amplitude, 1.97}, 0, 8}]