5.设螺旋形弹簧一圈的方程为x=acos t,y=asin t,z=kt,其中0≤t≤2π,它的线密度ρ(x,y,z)= x^2+y^2+z^2.求:

(1) 螺形 spring形弹簧关于 $x$ 轴的转动惯量为： \[ \boxed{\frac{2\pi a^2 \sqrt{a^2 + k^2}{3} \left(3a^2 + 4\pi^2 k^2\right) \] (2) 重心坐标为： \[ \boxed{\left( \frac{6a k^2}{3a^2 + 4\pi^2 k^2}。 (3)。 \[ \boxed{ \[ \[ \boxed{ \[ \[ \[ \[ \boxed{ \[ \frac{6\pi k^2\pi^2} \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \[ \boxed{ \] \[ \[ \boxed{ \[ \boxed{ \[ \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \[ \boxed{ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \[ \boxed{ \boxed{ \boxed{ \boxed{ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \boxed{ \[ \[ \[ \boxed{ \[ \boxed{ \[ \[ \[ \boxed{ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \boxed{ \[ \[ \[ \[ \[ \[ \[ \[ \。 \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \[ \2\[ \[ \[ \[ \[ \[ \2 \[ \[ \[ \[ \[ \[ \[ \[ \33\3\ \ \ \3\[ \2\ \\0\2\2\[ \[ \[ \3\