PHYS-1500 PHYSICAL MODELING
FALL 2006
9/08/2006, Class 4: Simple Harmonic Test
NAME ________ANSWERS______________
I. Directions for setting up the “trial spreadsheet”
In cell E3, enter the formula, =MAX(C4:C403)
In cell H3, enter the formula, =2*PI()/F3
In cell I2, enter the formula, =MAX(B4:B403)
In cell J2, enter the formula, =MIN(B4:B403)
In cell K2, enter the formula, =(I2+J2)/2
In cell C4, enter the formula, =B4-$K$2
In cell D4, enter the formula, =$E$3*COS($H$3*A4+$G$3)
Then copy these down through row 403
Graph both the data and the model, as functions of time, on the same graph.
Adjust A, T, and to get the best fit to the data.
What are the best values?
A = 1.02 ×10-1 m
T = 1.555 s
 = – 0.29 radians
There is more on the back of this sheet.
Simple Harmonic Motion
1.50E-01
1.00E-01
y (m)
5.00E-02
data
0.00E+00
0.00E+0 2.00E+0 4.00E+0 6.00E+0 8.00E+0 1.00E+0 1.20E+0 1.40E+0
0
0
0
0
1
1
1
-5.00E-02 0
model
-1.00E-01
-1.50E-01
t (s)
II. Now set up model 3.1, on page 73 of the text book.
Use:
t = 0.1 s
x0 = 3.0 cm
v0 = 1.0 cm/s
k = 1.0 dyne/cm
m = 4.0 g
Sketch the graph of the analytic solution and the Euler solution on the same graph.
5
4
3
2
1
0
-1 0
5
10
-2
-3
-4
-5
t (s)
15
x(t) cm
Anal. x(t) cm
Change k to 16 dyne/cm and sketch the same graph.
25
20
15
10
5
x(t) cm
Anal. x(t) cm
0
-5 0
5
10
-10
-15
-20
t (s)
15