2. SLIDESMANIA.
At rest: my” + ky = 0
0.75 λ2 + 72 λ = 0
W = ky
k = 72 lbf/ft
m = W/g
m = 0.75 slug G.S.
1.
2.
k(1/3ft)
24lbf
2
f
32ft/s
24lb
m
A mass weighing 24 pounds stretches a spring by 4 inches. Initially, the mass is
released from rest from a point 3 inches above the equilibrium position with zero
initial velocity. Find the equation of motion. What is the position of the mass after 2
min.?
0.75
72
λ
i
6
4
λ
t
6
Bsin4
t
6
Acos4
y(t)
t
6
Bcos4
6
4
t
6
Asin4
6
4
y'
3. SLIDESMANIA.
at t = 0, y = -1/4 ft P.S.
at t = 2 min. or 120 sec,
at t = 0, y’ = 0
1.
2.
A mass weighing 24 pounds stretches a spring by 4 inches. Initially, the mass is
released from rest from a point 3 inches above the equilibrium position with zero
initial velocity. Find the equation of motion. What is the position of the mass after 2
min.?
Bsin(0)
Acos(0)
4
1
4
1
A
Bcos(0)
6
4
Asin(0)
6
4
0
0
B
t
6
cos4
4
1
y(t)
(120)
6
cos4
4
1
y
ft.
0.1743
y
4. SLIDESMANIA.
An 8-pound weight stretches a spring by 2 ft. The damping force is equivalent to 2
times the instantaneous velocity. The weight is released from the equilibrium position
with an upward velocity of 3 ft/s.
W = kso G.S.
m = W/g at t = 0, y = 0
P.S.
1.
2.
a. Determine the equation of motion.
k(2ft)
8lb f
/ft
4lb
k f
2
f
32ft/s
8lb
m
slug
4
1
m
0
ky
cy'
my"
0
4
2λ
λ
4
1 2
II.
Case
4
λ
4t
2
1 t)
C
(C
y(t)
e
4t
2
2
1
4t
C
t)
C
(C
4
y'
e
e
4(0)
2
1 (0))
C
(C
0
e
0
C 1
3
-
y'
0,
t
at
4(0)
2
C
3
e
3
C 2
4t
3t
y(t)
e
0
16
8λ
λ2
5. SLIDESMANIA.
An 8-pound weight stretches a spring by 2 ft. The damping force is equivalent to 2
times the instantaneous velocity. The weight is released from the equilibrium position
with an upward velocity of 3 ft/s.
1.
2.
b. What type of damping describes the motion? Critically damped oscillation.
c. Plot the motion of weight.
The amount of time it takes for the
motion to decay is much faster than
other oscillations.
