Buffon Needle

TUGAS

TEKNIK SIMULASI

Program Simulasi Buffon Needle

Oleh :

FERRY ISWONO

NRP. 1209 100 059

Jurusan Matematika

Fakultas Matematika dan Ilmu Pengetahuan Alam

Institut Teknologi Sepuluh Nopember

Surabaya

2012

DEKSRIPSI BUFFON NEEDLE

Dalam percobaan Buffon Needle, jarum dengan panjang (l), di jatuhkan secara acak

pada sebuah papan bidang datar bergaris sejajar dengan jarak (d). Untuk pemecahan secara

teoritis panjang jarum (l), dibatasi lebih kecil atau sama dengan jarak (d). Jika percobaan ini

dilakukan berulang-ulang, maka perkiraan peluang jarum menyentuh sebuah garis yaitu P,

dapat diperoleh dari perbandingan jumlah percobaan dimana sebuah garis tersentuh, N l

dengan jumlah total percobaan NT:

P=N l

NT

Selain itu, posisi jarum juga harus bisa diletakkan secara acak, relative terhadap garis

sejajar pada papan. Untuk itu ditetapkan posisi jarum adalah unik, yaitu titik tengah jarum

(m) dan sudut yang terbentuk antara jarum dengan garis (θ). Supaya jarum mempunyai posisi

yang acak maka variabel m dan θ harus berupa variabel acak uniform.

Untuk menyederhanakan bentuk model maka hanya akan ditinjau dari dua garis

sejajar seperti pada gambar diatas. Lokasi m ditetapkan dan dicari garis mana yang

mempunyai jarak terpendek dengan m. Karena posisi acak adalah simetri maka hanya ditinjau

dari setengah jarak dua garis tersebut ( d2 ). Sehingga jarak dari m ke garis terdekat (a) adalah

variabel acak juga. Karena simetris maka θ adalah sebuah variabel acak uniform pada

variabel 0 sampai π radian.

Model Flowchart dari Percobaan Buffon Needle

Listing Program Simulasi Buffon Needle dengan Matlab

function varargout = AlgBuffonNeedle(varargin)% ALGBUFFONNEEDLE M-file for AlgBuffonNeedle.fig% ALGBUFFONNEEDLE, by itself, creates a new ALGBUFFONNEEDLE or raises the existing% singleton*.%% H = ALGBUFFONNEEDLE returns the handle to a new ALGBUFFONNEEDLE or the handle to% the existing singleton*.%% ALGBUFFONNEEDLE('CALLBACK',hObject,eventData,handles,...) calls the local% function named CALLBACK in ALGBUFFONNEEDLE.M with the given input arguments.%% ALGBUFFONNEEDLE('Property','Value',...) creates a new ALGBUFFONNEEDLE or raises the% existing singleton*. Starting from the left, property value pairs are% applied to the GUI before AlgBuffonNeedle_OpeningFcn gets called. An% unrecognized property name or invalid value makes property application% stop. All inputs are passed to AlgBuffonNeedle_OpeningFcn via varargin.%% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one% instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES % Edit the above text to modify the response to help AlgBuffonNeedle % Last Modified by GUIDE v2.5 06-Mar-2012 14:07:00 % Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @AlgBuffonNeedle_OpeningFcn, ... 'gui_OutputFcn', @AlgBuffonNeedle_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []);if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1});end if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});else gui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT % --- Executes just before AlgBuffonNeedle is made visible.function AlgBuffonNeedle_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject handle to figure

% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to AlgBuffonNeedle (see VARARGIN) % Choose default command line output for AlgBuffonNeedlehandles.output = hObject; % Update handles structureguidata(hObject, handles); % UIWAIT makes AlgBuffonNeedle wait for user response (see UIRESUME)% uiwait(handles.figure1); % --- Outputs from this function are returned to the command line.function varargout = AlgBuffonNeedle_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structurevarargout{1} = handles.output; function TxtL_Callback(hObject, eventdata, handles)% hObject handle to TxtL (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of TxtL as text% str2double(get(hObject,'String')) returns contents of TxtL as a double % --- Executes during object creation, after setting all properties.function TxtL_CreateFcn(hObject, eventdata, handles)% hObject handle to TxtL (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function TxtNt_Callback(hObject, eventdata, handles)% hObject handle to TxtNt (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of TxtNt as text% str2double(get(hObject,'String')) returns contents of TxtNt as a double

% --- Executes during object creation, after setting all properties.function TxtNt_CreateFcn(hObject, eventdata, handles)% hObject handle to TxtNt (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function TxtD_Callback(hObject, eventdata, handles)% hObject handle to TxtNt (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of TxtNt as text% str2double(get(hObject,'String')) returns contents of TxtNt as a double % --- Executes during object creation, after setting all properties.function TxtD_CreateFcn(hObject, eventdata, handles)% hObject handle to TxtNt (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function TxtP_Callback(hObject, eventdata, handles)% hObject handle to TxtP (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of TxtP as text% str2double(get(hObject,'String')) returns contents of TxtP as a double % --- Executes during object creation, after setting all properties.function TxtP_CreateFcn(hObject, eventdata, handles)% hObject handle to TxtP (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');

end % --- Executes on button press in BtnRun.function BtnRun_Callback(hObject, eventdata, handles)% hObject handle to BtnRun (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) ferry = guidata(gcbo) l = str2num(get(ferry.TxtL, 'String'));d = str2num(get(ferry.TxtD, 'String'));Nt = str2num(get(ferry.TxtNt, 'String')); Ni = 0; for i=0:Nt r1=rand; a=(d/2)*r1; r2=rand; t=pi*r2; if a<=((l/2)*sin(t)) Ni=Ni+1; endendP=Ni/Nt; set(ferry.TxtP,'String',P); % --- Executes on button press in BtnSelesai.function BtnSelesai_Callback(hObject, eventdata, handles)% hObject handle to BtnSelesai (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) close();

HASIL PROGRAM

Untuk N=5000 , dgn l = 10 dan d = 20

Dengan menggunakan program simulasi Buffon Needle diatas, diperoleh:

masukkan nilai l = 10

masukkan nilai d = 20

masukkan nilai N = 5000

P = 0.3206

Untuk N=1000, dgn l = 10 dan d = 20

Dengan menggunakan program simulasi Buffon Needle, diperoleh:




P =

0.3450






P =

0.3147






P =

0.2975

KESIMPULAN:

Walaupun nilai N yang diinputkan besar atau kecil, tetapi tidak terjadi perbedaan nilai

yang besar di P. karena nilai yang di ambil oleh distribusi seragam antara 0 – 1 untuk

menghitung r1 dan r2.

Buffon Needle

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Transcript of Buffon Needle