Question

MATLAB CODE: Consider the second order system x(0)-o y (o)-o G -9.8m/s let M 5g θ 350 Vo 40m/s Plot x vs y -0.5 g/m

Answer 1

The question is a Nonlinear Differential Equation with Initial Conditions given. This can be solved using the Symbolic Toolbox of MATLAB:

1. First, the code for solving x(t) is given below. Also, we convert all the variables into S.I units.

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MATLAB code for solving for the variable x(t):

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M=5;
alpha=0.5;

G=-9.8;

v0=40;
theta=35;

syms x(t)

D=diff(x);
ode = (M*diff(x,t,2)+alpha*(diff(x,t))^2) == 0;
cond1 = x(0) == 0;
cond2 = D(0) == v0*cosd(theta);

cond=[cond1 cond2];

X(t) = dsolve(ode,cond);

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The output comes out to be:

X=10*log((1152854012943651*t)/35184372088832 + 10) - 10*log(10)

which becomes

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MATLAB code for solving for the variable y(t):

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M=5;
alpha=0.5;

G=-9.8;

v0=40;
theta=35;

syms y(t)

D=diff(y);
ode = (M*diff(y,t,2)+alpha*(diff(y,t))^2) == G*M;
cond1 = y(0) == 0;
cond2 = D(0) == v0*sind(theta);

cond=[cond1 cond2];

Y(t) = dsolve(ode,cond);

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In the output MATLAB displays a warning that the explicit solution could not be found

Y= [emp sym]

This may be because of the wrong questionf for the case of y.

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