1. 1. Numerical Analysis Project Projectile Motion Using MATLAB
2. 2. Group Members Awais Ahmad (Group Head) 12- EE(E&T)-11 M. Ahmed Waqas 12- EE(E&T)-031 Adeel Ahmed 12- EE(E&T)-004 Faheem Khan 12-EE(E&T)-013 Farhan Abbas 12-EE(E&T)-016
3. 3. Contents Euler Method Physical Aspects of this Method Practical Implementation Code and Input Output Conclusion
4. 4. Euler Method The Euler method is y{n+1} = y(n) + hf(t(n),y (n)). so first we must compute f(t(0), y(0)). In this simple differential equation, the function f is defined by f(t,y) = y
5. 5. Physical Aspects of This Method Measuring the Period of Oscillation Measuring the Velocity of Projectile Motion Measuring the Current and Voltage of RC,RL,RLC Circuits. Measuring the torque of motor In short any 1st Order IVP can be solved
6. 6. Practical Implementation (Projectile Motion) Solution By Theoretical Implementation Projectile System By using MATLAB
7. 7. Theoretical Implementation Given that:- mV` =Fg + Fr ;where as Fg=-m*g , Fr=-kV|V| Also , g=9.8ms-2 ; k=0.002kg/m ; m=0.11kg ;V0=8ms-1 As |V|={ +V -V } By Putting Values and Simplifying we have 1st Order Differential Equation V`= - 9.8 - 0.1818 V2
8. 8. Using MATLAB
9. 9. Output
10. 10. Graphical Representation