=+You are asked to apply (P3.11.a) to Equation (3.3) recast in the first-order form:

M????̇ + C???? + Kq = p(t)

ẋ = ???? (P3.11.b)

and show that it leads to a time-marching scheme described by the following equations:

⎧

⎪

⎪

⎨

⎪

⎪

⎩

(

K + 2

????t C + 4

????t2 M

)

qn+1 = gn+1

????n+1 = 2

????t

(qn+1 − qn) − ????n an+1 = 2

????t

(????n+1 − ????n) − an

(P3.11.c)

with the right-hand side:

gn+1 = pn+1 + C

(

????n +

2

????t xn

)

+ M

(

an +

4

????t

????n +

4

????t2 xn

)

(P3.11.d)