Question

I'm trying to solve this differential equations by using matlab and I've got a plot from the code attached. But I wanna get a plot of completely sinusoidal form. If I can magnify the plot and expand x-axis, maybe we can get the sinusoidal form. So help me with this problem by using matlab. Example is attached in below. One is the plot from this code and another is example.

function second_order_ode2

t=[0:0.001:1];

initial_x=0;

initial_dxdt=0;

[t,x]=ode45(@rhs,t,[initial_x initial_dxdt]);

plot(t,x(:,1))

xlabel('t')

ylabel('x')

function dxdt=rhs(t,x)

dxdt_1=x(2);

dxdt_2=(-50*x(2)-1000*x(1)+61.25+((1-cos(4*pi*10*t))/2).*(47380*x(1).^3-7428*x(1).^2+366*x(1)-7));

dxdt=[dxdt_1;dxdt_2];

end

end

Figure 파일(E) 편집 보기 삽입ⓛ 둘 데스크탑(D) 창W 도움말(H) 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p Ul moving bar was 20 mm from the fixed yoke 0.012 Time stepping method(FEM) Proposed method 0.010 " 0.008 E 0.00 0.004 0.00EE -0.002 -0.004し 0.0 0.2 1.0 0.6 0.4 0.8 Time [s]

Answer 1

open matlab figure and double click on axis

change the axes limits so that sinusoidal waveform of given magnitude can be identified.

Figures Figure 1 X File Edit View Insert Tools Debug Desktop Window Help Figure 1 0.0616 0.0614 H 0.0612 - 0.061 H x 0.06089- 0.0606 0.0604 0.0602 0.060 02 04 15 06 07 0.8 9 0.1 0.3 t Property Editor- Axes Title XAxis Y Axis Z Axis Font More Properties... Y Label: Ticks.. to 0616 Auto Y Limits Colors: Reverse xYz Y Scale lincar Grid Y Axis Location: left Box Box 07:14 Type here to search ENG 2.06-2019

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to expand x axis scale go to axis editor and open ticks so that X tick locations can be selected by step by.

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Figures-Fiqure 1 Edit Axes Ticks X File Edit View Debug Desktop Window Insert Tools Help X Axis Y Axis Z Axis Figure 1 X Tick Locations X Tick Labels: O Auto O Auto 0.0616 O Manual O Manual OStep by 0.05 0.0614H Locations Labels 0.0612 - 0.1 0.1 Insert 0.15 0.15 0.061 H Delete 0.25 0.25 x 0.06089- 0.3 0.3 3 0.35 0.0606 0.4 0.4 0.45 45 0.0604 nst 0.55 0.6 0.6 0.0602 0.65 0.65 0.060 0.1 Show minor ticks 0.15 02 0.25 03 0.35 0.45 0.5 0.55 0.6 04 t Apply OK Cancel Property Editor - Axes Title X Axis y Axis Z Axis Font More Properties.. X Label Ticks... Auto X Limits to 1 Colors: X Scale Reverse Grid: XYz lincan X Axis Location: bottom Box Box 07:21 Type here to search ENG 0-06-2019

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to expand X axis 2 nd line of code can be written as

t=[Xstart:0.001:Xlimit];

Xstart may be from 0 or specified value.

Xlimit is the extended value

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final code

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function second_order_ode2
t=[0:0.001:10];
initial_x=0;
initial_dxdt=0;
[t,x]=ode45(@rhs,t,[initial_x initial_dxdt]);
plot(t,x(:,1))
xlabel('t')
ylabel('x')
function dxdt=rhs(t,x)
dxdt_1=x(2);
dxdt_2=(-50*x(2)-1000*x(1)+61.25+((1-cos(4*pi*10*t))/2).*(47380*x(1).^3-7428*x(1).^2+366*x(1)-7));
dxdt=[dxdt_1;dxdt_2];
end
end

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