MATHEMATICA – Computer Simulation R.C. Verma Physics Department Punjabi University Patiala – 147 002 PART IX- Computer Simulation Mechanics. INTRODUCTION. Traditionally physics teaching comprises of theory lectures based on analytical techniques and conventional laboratory experiments.
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MATHEMATICA – Computer Simulation
R.C. Verma
Physics Department
Punjabi University
Patiala – 147 002
PART IX- Computer Simulation
Mechanics
For practical purposes of PC into physics we need to answer:-
i) Number awareness
ii) Experimental skills
iii) Analytic skills
iv) Scales and estimations
v) Approximations skills
vi) Numerical skills
vii) Intuition & large problem skills
Physics → Algorithm → Program → Results
Identify the input variables:-like parameters of a physical systeminitial conditions of the`system and time interval step size of time evolution.
Identify the output variables:-solution of the problem.
Construct the equations to connect the input variables to the output variables.
Re-express the equations using numerical techniques.
Write algorithm/flowchart to solve the problem.
Develop Programs (I/O, common arithmetic operations and logical structures: Sequential, Repetitive and Selective).
Execute the program on a computer.
Run computer experiments to study effects of:
Clear["Global`*"]
(* Find Analytic solution *)
k = 3.0;(* spring constant *)
m = 1.0;(* mass attached to the spring *)
w0 = Sqrt[k/m];
c = 0.5;
damp = c/m;
x0=1.0; v0 = 1.0;(* initial conditions *)
tmin = 0;tmax = 5;
ndsol=DSolve[ {x''[t]+damp*x'[t]+w0^2 x[t]==0,
x[0]==x0, x'[0]==v0}, x[t], t]//Chop//Flatten
(* Plot the solution for a given time interval *)p1= Plot[ x[t]/.ndsol, {t,tmin, tmax}, AxesLabel->{"t->", "x"}, PlotLabel->"Harmonic Motion"]