From 01b563a0c2f436a15d0d41aa160a52f125e84ed3 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 31 Oct 2017 16:26:04 -0400 Subject: [PATCH] fix numbering hw4 --- HW4/README.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/HW4/README.md b/HW4/README.md index ae98f2c..c4e170f 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -15,7 +15,7 @@ with \`\`\` and document your code in the README.md file* c. Submit clone repo link to [https://goo.gl/forms/gFNxhNM4qJJKj8hE3](https://goo.gl/forms/gFNxhNM4qJJKj8hE3) -2. Create the 4x4 and 5x5 [Hilbert matrix](https://en.wikipedia.org/wiki/Hilbert_matrix) as H. Include the following results in your +**2\.** Create the 4x4 and 5x5 [Hilbert matrix](https://en.wikipedia.org/wiki/Hilbert_matrix) as H. Include the following results in your README before 10/26 by midnight: a. What are the 2-norm, frobenius-norm, 1-norm and infinity-norm of the 4x4 and 5x5 @@ -29,22 +29,22 @@ README before 10/26 by midnight: ### P3-4 Due 10/30 -3. Create a Cholesky factorization function called `chol_tridiag.m` that takes 2 vectors +**3\.** Create a Cholesky factorization function called `chol_tridiag.m` that takes 2 vectors as inputs and calculates the Cholseky factorization of a tridiagonal matrix. The output should be 2 vectors, the diagonal and the off-diagonal vector of the Cholesky matrix. - ```[d,u]=chol_tridiag(e,f);``` + ```[d,u]=chol_tridiag(e,f);``` -4. Use the output from `chol_tridiag.m` to create a forward substitution and +**4\.** Use the output from `chol_tridiag.m` to create a forward substitution and back-substitution function called `solve_tridiag.m` that provides the solution of Ax=b given the vectors from the output of [d,u]=lu_tridiag(e,f). *Note: do not use the backslash solver `\`, create an algebraic solution* - ```x=solve_tridiag(d,u,b);``` + ```x=solve_tridiag(d,u,b);``` ![Spring-mass system for problem 5](./figures/mass_springs.png) -5. Create the stiffness matrix for the 4-mass system shown above +**5\.** Create the stiffness matrix for the 4-mass system shown above for cases a-c. Calculate the condition of the stiffness matrices. What is the expected error when calculating the displacements of the 4 masses? Include the analysis and results in your README. @@ -54,18 +54,18 @@ when calculating the displacements of the 4 masses? Include the analysis and res c. K1=K3=K4=1000 N/m, K2=1000e-12 N/m -6. Use `chol_tridiag.m` and `solve_tridiag.m` to solve for the displacements of hanging +**6\.** Use `chol_tridiag.m` and `solve_tridiag.m` to solve for the displacements of hanging masses 1-4 shown above in 5a-c, if all masses are 1 kg. ![Spring-mass system for analysis](./figures/spring_mass.png) -7. In the system shown above, determine the three differential equations for the position +**7\.** In the system shown above, determine the three differential equations for the position of masses 1, 2, and 3. Solve for the vibrational modes of the spring-mass system if k1=10 N/m, k2=k3=20 N/m, and k4=10 N/m. The masses are m1=1 kg, m2=2 kg and m3=4 kg. Create a function, `mass_spring_vibrate.m` that outputs the vibration modes and natural frequencies based upon the parameters, k1, k2, k3, and k4. -8. The curvature of a slender column subject to an axial load P can be +**8\.** The curvature of a slender column subject to an axial load P can be modeled by