Download Presentation
## METHOD OF UNDETERMINED COEFFICIENTS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Solve the following differential equation using method of**undetermined**TRY THIS ALSO…..**1 2 3**METHOD OF SOLUTION**Identify a and f(x) Substitute to general solution: Determine y1 and y2 (obtain from general solution of homogeneous equation y=Ay1+ By2) Evaluate u and v Evaluate Wronskian,**Other question**1 2**It called second order linear differential equation with**variable coefficient • Euler equation: • Use substitution thus , and to reduce: • Solve it and get the answer in term of x and y From variable coefficient To constant coefficient**Solve it……**1 2 3 4**In equilibrium, [figure 1(b)] according to Newton's First**Law, the resultant force is zero, So: • In this case, the spring stretched as far as s. according to Hooke's law • From 1 and 2 obtain • Next in equilibrium, the mass is pulled down a distance x and released. According to Hooke's law this spring elongation when F is: 1 2 3 4**According to Newton’s Second Law:**• From equation 4, • When the resistance is negligible, the resistance equal to zero, so equation 5 becomes 5 6**From equation 6 or is called second order linear homogeneous**differential equation: • From 7, get the general solution as 7 Equation of Motion**The period of free vibrations**• Frequency is • If initial condition is given, find the value of A and B in equation of motion.