Question

3. [10 pts) Consider a familiar horizontal ideal spring-mass system. The solutions for both the velocity and position of the mass are oscillatory. Write down the second-order differential equa- tion which describes the position of the mass. Although this differential equation does have an analytic solution, use Mathematica to find and plot x(t) numerically, using NDSolve. Pick convenient values for mass and spring constant, and assume the object begins at rest at some finite positive position. For these values, use your plot to determine the period, T, of the motion. Check it with what you know about the analytic solution. For help using NDSolve, check out this screencast: http://youtu.be/zK06vOwokdI. (If you don't use Mathematica, various integration algorithms are built into a lot computational tools e.g., Runge-Kutta, or Dorman-Prince.)

Answer 1

Ans:- let mass of object be lkg and spring constant be INm, then from Newton's and how we get net force as F = -ks => m d m = -Kx. This is and order differential equation : The particle is starting from rest and starting from anon-zero Position, we can write alo)=1,110) -0. now we solve this Osing ND solve [n(4)]:S: ND solve [ca!(+3 +417)-0, ) = 1, x'(0 :0),, (,- 10/0)] out 1434 fa a interpolating teachiono non Domain {-10,103 % elp scalar IN 16): plor {Evaluare [4 (t)).s], [t, -10,10), plo + Style ->thi ceļ. ve OUTTO). 1. SI 5 10 From Graph, the distance b/w 2 adjacent peak is 6.21 sec. we have started by assuming Spring Constant as IN/m and may as ikg. Angular Frequency = T = 211 m/k =25