110年 - 110 國立中央大學_碩士班招生考試_土木工程學系/力學與結構工程組(一般生):工程數學#103870

(1) If the mass displacement y(t) (solid line) is shown in following figure with y(0) = 1 m, y'(0)=0 m/s, please find mass m= ? kg (10%) 

(2) If the upper system has an applied external force r(t)= sinωt, please find the to have the maximum amplification (15%)

(3) If the upper applied external force r(t)= sin2t which only exists at 0 ≤t≤ π , please find the related mass displacement y(t) by Laplace transform (15%)

(4) If
for the upper system which is assumed as an undamped and homogeneous one, please show the solution of y(t) in series form (10%)

3.求方向導數(25%)