#$&*
course MTH-279
07/29 around 11:00PMJust turning in some problems I did leading up to test two.
Query 18 Differential Equations
*********************************************
Question: A 10 kg mass stretches a spring 30 mm beyond its unloaded position. The spring is pulled down to a position 70 mm below its unloaded position and released.
Write and solve the differential equation for its motion.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
F = k delta x
aka mg = k deltax
---
k = mg/deltax
k = (10)(9.8)/(0.03)
k = (3,266.67 N/M
-----
10y’’ + 0y’ + 3266.67y = 0
y’’ + 326.67 = 0
x^2 + 326.67 = 0
x^2 = -326.67
sqrt x^2 = sqrt -326.67
use, i^2 = -1 -> i = sqrt -1
----
x^2 = -326.67 -> (-1)326.67
x^2 = i^2 (326.67)
sqrt x^2 = sqrt 326.67
x = I sqrt 326.67
x = 18.07i
----
general solution for complex root is y(t) = C1cos(lambda t) + C2 sin(lambda t)
x = lambda = 18.07i
y(t) = C1 cos (18.07t) + C2 sin(18.07t)
---
y(0) = 0.04m
----
0.04 = C1 cos(18.07(0)) + C2 sin (18.07(0))
0.04 = C1 + 0
C1 = 0.04
---
y’(0) = 0 (spring released)
y’ = -C1sin(18.07t) + C2cos(18.07t)
0 = -0.04sin(0) + C2cos(0)
0 = C2
----
y(t) = 0.04cos(18.07t)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution:
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):OK
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course MTH-279
07/29 around 11:00PMJust turning in some problems I did leading up to test two.
Query 18 Differential Equations
*********************************************
Question: A 10 kg mass stretches a spring 30 mm beyond its unloaded position. The spring is pulled down to a position 70 mm below its unloaded position and released.
Write and solve the differential equation for its motion.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
F = k delta x
aka mg = k deltax
---
k = mg/deltax
k = (10)(9.8)/(0.03)
k = (3,266.67 N/M
-----
10y’’ + 0y’ + 3266.67y = 0
y’’ + 326.67 = 0
x^2 + 326.67 = 0
x^2 = -326.67
sqrt x^2 = sqrt -326.67
use, i^2 = -1 -> i = sqrt -1
----
x^2 = -326.67 -> (-1)326.67
x^2 = i^2 (326.67)
sqrt x^2 = sqrt 326.67
x = I sqrt 326.67
x = 18.07i
----
general solution for complex root is y(t) = C1cos(lambda t) + C2 sin(lambda t)
x = lambda = 18.07i
y(t) = C1 cos (18.07t) + C2 sin(18.07t)
---
y(0) = 0.04m
----
0.04 = C1 cos(18.07(0)) + C2 sin (18.07(0))
0.04 = C1 + 0
C1 = 0.04
---
y’(0) = 0 (spring released)
y’ = -C1sin(18.07t) + C2cos(18.07t)
0 = -0.04sin(0) + C2cos(0)
0 = C2
----
y(t) = 0.04cos(18.07t)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution:
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):OK
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
#$&*
course MTH-279
07/29 around 11:00PMJust turning in some problems I did leading up to test two.
Query 18 Differential Equations
*********************************************
Question: A 10 kg mass stretches a spring 30 mm beyond its unloaded position. The spring is pulled down to a position 70 mm below its unloaded position and released.
Write and solve the differential equation for its motion.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
F = k delta x
aka mg = k deltax
---
k = mg/deltax
k = (10)(9.8)/(0.03)
k = (3,266.67 N/M
-----
10y’’ + 0y’ + 3266.67y = 0
y’’ + 326.67 = 0
x^2 + 326.67 = 0
x^2 = -326.67
sqrt x^2 = sqrt -326.67
use, i^2 = -1 -> i = sqrt -1
----
x^2 = -326.67 -> (-1)326.67
x^2 = i^2 (326.67)
sqrt x^2 = sqrt 326.67
x = I sqrt 326.67
x = 18.07i
----
general solution for complex root is y(t) = C1cos(lambda t) + C2 sin(lambda t)
x = lambda = 18.07i
y(t) = C1 cos (18.07t) + C2 sin(18.07t)
---
y(0) = 0.04m
----
0.04 = C1 cos(18.07(0)) + C2 sin (18.07(0))
0.04 = C1 + 0
C1 = 0.04
---
y’(0) = 0 (spring released)
y’ = -C1sin(18.07t) + C2cos(18.07t)
0 = -0.04sin(0) + C2cos(0)
0 = C2
----
y(t) = 0.04cos(18.07t)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution:
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):OK
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!#*&!
&#Your work looks good. Let me know if you have any questions. &#