PHYS-1500 PHYSICAL MODELING
FALL 2006
9/12/2006, Class 5: Runge-Kutta Method
NAME ________ANSWERS______________
1. Construct the Runge-Kutta spreadsheet 3.2 as described in the lessons beginning on page 78
of the textbook.
2. Construct spreadsheet 3.3 by adding one column to spreadsheet 3.2.
3. Construct spreadsheet 3.4 by adding two columns to spreadsheet 3.3.
4. Quantify the error associated with the Runge-Kutta method as indicated in section 3. c. of
exercise 3.2, on page 83 of the textbook.
t (s)
Error (m) @ t = 1 s
0.1
1.2 ×10-8
0.01
8.6 ×10-13
0.001
– 3.6 ×10-15
5. Now change k from 1 to 16 N/m, as you did for the Euler model. Sketch the resulting graph.
The graph shows no noticeable difference.
x (m)
4
3
2
1
x(anal)
0
0
2
4
6
-1
-2
-3
-4
t (s)
8
10
12
x
6. Do problem 4 (a) on page 85. Use the Runge-Kutta method.
Time until collision = 554400 s = 154 hr = 6.41667 days = 6 days and 10 hours.
Speed at collision = 0.0195 m/s = 1.95 cm/s = 0.044 mi/hr. A modest jolt.
Separation vs. time
1200
1000
r (m)
800
600
400
200
0
0
100000 200000 300000 400000 500000 600000 700000
t (s)