In solving the beam equation, you determined that the general solution is q₁x²+x. Given that y(1) =3 determine 9₁ 12 2. The particular solution x, for x + 2x=4e-³ i Ip=92e-3 3. In calculating the Laplace transform L{(1+2) H(1-5)} using the formula Lif(t-a)H(1-a)} = "L{f(t)} on the Laplace sheet you calculated that the f(t) referred to in this formula is f(t) = **1+qs 4. The Laplace transform 5 +4s +6 can be expressed as Le[qssin(q6t)+q7cos(**)]} 5. The state-space representation for 2x + 4x + 5x = 10e" is = 6. Calculate the eigenvalue of the state-space coefficient matrix-7a-2a using the methods demonstrated in your lecture notes (Note that is a positive constant, do not assume values for a). If your eigenvalues are real and different, let λ be the smaller of the two eigenvalues when comparing their absolute values, for example, if your eigenvalues are -3 and -7, their absolute values are 3 and 7 with 3 < 7 and ₁=-3. If your eigenvalues are a complex conjugate pair, let ₁ be the eigenvalue with the positive imaginary part. The eigenvalue you must keep is ₁ =q₁a + 9₁2 a j Note that if is real valued that 912 = 0 7. The general solution of a non homogeneous state-space equation is given below. Use the initial conditions to determine the value of C₁. [] = 9₁²) [2¹] + G₂ -² » [-2 } ] + [Q]• given x(0)=0, x'(0) = 2 You calculated that C₁ = 913+914j Note that if C₁ is a real number that 14 = 0.