# Question: the following equation can be used to model the deflection...

###### Question details

The following equation can be used to model the deflection of a sailboat mast subject to a wind force:

= (L-z)

Where E is the modulus of elasticity, L is mast length, I the second moment of area and f(z) is the wind force depending on the height z and is given by:

f(z) = =

Calculate the deflection of the mast using the 4th order Runge-Kutta method with y=0 and y'=0 at z=0. Perform the first analysis with n divisions of the length L to define the step (see the table below for your assigned value of n). Repeat the analysis with twice the number of divisions(i.e 2n divisions) and produce a graph of the deflection and curvature vs. the height for the two cases.

Data Set |
E(N/m²) |
I(m⁴) |
L(m) |
Number of Divisions, |

1 |
1.08E+08 |
0.05 |
29 |
6 |

2 |
1.34E+08 |
0.03 |
42 |
7 |

3 |
1.18E+08 |
0.04 |
41 |
8 |

4 |
1.01E+08 |
0.05 |
36 |
9 |

5 |
1.25E+08 |
0.06 |
24 |
10 |

6 |
1.32E+08 |
0.07 |
41 |
6 |

7 |
1.50E+08 |
0.08 |
19 |
7 |

8 |
1.05E+08 |
0.04 |
39 |
8 |

9 |
1.10E+08 |
0.05 |
14 |
9 |

10 |
1.44E+08 |
0.06 |
35 |
10 |

11 |
1.05E+08 |
0.04 |
40 |
11 |

12 |
1.10E+08 |
0.06 |
36 |
9 |

13 |
1.05E+08 |
0.07 |
28 |
8 |

14 |
1.25E+08 |
0.05 |
30 |
12 |