1. Using estimates of rainfall, evaporation, and water consumption, the town eng

Question

1. Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time

Where V is the water volume in liters, t is time in days, and r is the town’s consumption rate in liters per day. Write two user-defined functions. The first function should define function V(t) to evaluate V for any input of . The second function should use fzero to compute how long it will take for the water volume to decrease to x percent of its initial value of Liters. The inputs to the second function should be x and r. Test your functions for the case where x= 50 percent and r = 107 Liters/day.

2. We want to analyze the mass-spring system illustrated in the figure below for the case in which the weight W is dropped onto the platform attached to the center spring. If the weight is dropped from a height h above the platform, we can find the maximum spring compression x by equating the weight’s gravitational potential energy (h + x) W with the potential energy stored in the springs. Thus

Which can be solved for x as

And

Which gives the following quadratic equation to solve for x:

Create a function that computes the maximum compression x due to the falling weight. The function’s input parameters are k1, k2, d, W, and h. Test your function for the following two cases, using the values k1 = 104 N/m; k2 = 1.5 × 104 N/m; and d = 0.1 m.

W = 100 N        h = 0.5 m

W = 2000 N      h = 0.5 m

Use your function file to generate a plot of x versus h for 0h2 m. Use W = 100 N and the preceding values for k1, k2, and d.

Trying to figure out how this is done in MATLAB R2016. I can not figure out how to put it in as a function then do it as a command.

Please help

Explanation / Answer

1) Ans:

clear screen;
clear all;
close all;

x = input('Please enter the value of x: ');
r = input('Please enter the value of y: ');

fzero = 10^9; %%in litres %% defining the first function

syms t
solve((fzero*x/100)-(10^9)-(10^8*(1-exp(-t/100))) + (r*t) == 0)

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