Question

Problem 2: The following data of the velocity of a body is given as a function of time 24 33 Time (sec) Velocity (m/s) 17 28 0 21 26 223 a. Calculate the velocity in m/s at t= 22 sec using a quadratic polynomial interpolation through linear systems of equations. b. Set up the 9x9 matrix to solve all coefficients through quadratic spline interpolation (the matrix itself is the answer we're looking for, you do not need to solve it)

Answer 1

We have solved the given problem using quadratic spline interpolation.

We have doto net as follows: Time (t) 0 Velocity (0) 21 17 24 28 33 26 223 : The data quadratic polynomial interpolation for the given is given by { 0, Lt) = a + b + te ť id ost2p7 1(t) = ₂ (t) = Qutb it tęt it 17€ t€ 24 \U3 Lt) = az + b₂ t + es + id 242+526 where given by the constan unknown coefficients are 0,0) = 21 14 (17) = 28. = 0, = 21 q + 176, +289 G = 28 ų (17) = 28 a +17 b, +289 { = 28 (24)=33 = a +24b+ 576 'ę = 33 Uz (24) = 33 - az + 24 b3 + 576 Cz = 33. U3 (26) = 223 ) az +26 b3 +676 = 223 dis - du at t=17 = 6, +34 9 = b 2 + 34 a at t=24 =) b, +48 4 = bz + 48 g. de =) = 0

Solving these we get, a=21 , 6,=-478 A₂ =_66755 b. = 1634 Az = - 2247 62 = 95 = 96 = - 41. =0 Cos (t=22) = V2 (22) 17 ( 22<24 =-66755 + 16 34 x 22 - 48 x 484 = 171,75 m/s. 6 The co-efficiento matrix is given an, 11 1 0 0 17 0 289 0 0 0 1 0 0 17 0 0 289 0 0 0 0 24 576 0 0 - 0 1 24 576 0 0 0 0 0 0 0 0 34 0 - 0 26 676 -34 o o 48 01 +48 0 0 0 0 0 0 0 0 0 0