3-31-17
1a. t = 0 s
T = 1.5 s
Max speed = 42 cm/s or 0.42 m/s
vmax = ωA = 2π/T
A = vT/2π = (42 cm/s)(1.5 s) = 10 cm
6.28
b. x = Acos(2π(t)/T) = (10 cm)cos 2π(24 s)
1.5 s
= (10 cm)cos(100.53096) = 10 cm calculator: radian (rad)
2a. x = 3sin(πt/4) = 0, 2, 3, 2, 0, -2, -3, -2, 0, 2, 3
t = 0 – 10
x = 3sin(2πt/8) = 0, 2, 3, 2, 0, -2, -3, -2, 0, 2, 3
t = 0 – 10
x = 3cos(πt/4) = 3, 2, 0, -2, -3, -2, 0, 2, 3, 2, 0
t = 0 – 10
x = 3cos(2πt/8) = 3, 2, 0, -2, -3, -2, 0, 2, 3, 2, 0
t = 0 – 10 calculator: rad
b. d = 2cos(2πt) = 0.0 cm, -2.0 cm, 0.0 cm, 2.0 cm
t = 0.25 s, 0.50 s, 0.75 s, 1.0 s
c. v = 5sin(2πt) = 0, 0, -5, 0 cm/s
t = 0.0 s, 0.50 s, 0.75 s, 1.0 s
,d. 2cos(2π(1.5)) = -2 cm
5sin(2π(1.5)) = 0 cm/s
e. 10T = 0.17
T = 0.017 s
3a. A = 31 cm
f = 1.5 Hz
max displacement = 31 cm
b. 2π(1.5 Hz) = 9.424778 rad/s
vmax = (9.424778)(31 cm) = 290 cm/s
c. amax = (2πf)2A
= (9.424778)2(31 cm) = 2800 cm/s2
4a. 1.7 Hz
amax(vertical) = 0.17 m/s2
amax = (2πf)2A
A = amax = 0.17 m/s2 = 0.17 m/s2 = 1.49 x 10-3 m or 0.149 cm
(2πf)2 (10.681415)2 114.092626
b. vmax = 2πfA
= 2π(1.7 Hz)(1.49 x 10-3 m) = 1.6 x 10-2 m/s
,5a. f = 1/T = 1/0.04 s = 25 Hz
A = 0.04 m
amax = (2πf)2A = (2π(25 Hz))(0.04 m) = 990 m/s2
b. 1 m/s2 = 0.101971621 g
990 m/s2 0.101971621 g = 100 g
1 m/s2
6.
5.9 cm ?
1.3 kg 2.0 kg
F = -kx
F = mg
k = spring constant
x = stretch of spring
(1.3 kg)(9.81 m/s2) = K 5.9 cm
100 cm/m
12.753 = -K(0.059)
K = -216.15254
(2.0 kg)(9.81 m/s2) = -216.15254(x)
19.62 = -216.15254(x)
x = 9.08 cm
, 7a. 84 bpm
f = 84/60 = 1.4 Hz
b. T = 1/1.4 Hz = 0.71 s
8a. 0.700 kg
Spring constant = 18 N/m
Speed = 43 cm/s
KE = PE
mv2 = kA2
(0.700 kg)(0.43 m/s)2 = (18 N/m)(A)2
0.12943 = (18 N/m)(A)2
A2 = 0.007190556
A = 0.085 m or 8.5 cm
b. T = 2π√m/K
= 2π 0.700 kg = 1.2390608 s
18 N/m
v = (2π/t)[√(A2 – x2)] x = 0.35A A = 8.5 cm
= 2π {√8.5 cm2 – [(0.35)(8.5)]2}
1.2390608 s
= 5.0709257 s[√(72.25 – 8.850625)]
= (5.0709257 s)(7.962372) = 40 cm/s
1a. t = 0 s
T = 1.5 s
Max speed = 42 cm/s or 0.42 m/s
vmax = ωA = 2π/T
A = vT/2π = (42 cm/s)(1.5 s) = 10 cm
6.28
b. x = Acos(2π(t)/T) = (10 cm)cos 2π(24 s)
1.5 s
= (10 cm)cos(100.53096) = 10 cm calculator: radian (rad)
2a. x = 3sin(πt/4) = 0, 2, 3, 2, 0, -2, -3, -2, 0, 2, 3
t = 0 – 10
x = 3sin(2πt/8) = 0, 2, 3, 2, 0, -2, -3, -2, 0, 2, 3
t = 0 – 10
x = 3cos(πt/4) = 3, 2, 0, -2, -3, -2, 0, 2, 3, 2, 0
t = 0 – 10
x = 3cos(2πt/8) = 3, 2, 0, -2, -3, -2, 0, 2, 3, 2, 0
t = 0 – 10 calculator: rad
b. d = 2cos(2πt) = 0.0 cm, -2.0 cm, 0.0 cm, 2.0 cm
t = 0.25 s, 0.50 s, 0.75 s, 1.0 s
c. v = 5sin(2πt) = 0, 0, -5, 0 cm/s
t = 0.0 s, 0.50 s, 0.75 s, 1.0 s
,d. 2cos(2π(1.5)) = -2 cm
5sin(2π(1.5)) = 0 cm/s
e. 10T = 0.17
T = 0.017 s
3a. A = 31 cm
f = 1.5 Hz
max displacement = 31 cm
b. 2π(1.5 Hz) = 9.424778 rad/s
vmax = (9.424778)(31 cm) = 290 cm/s
c. amax = (2πf)2A
= (9.424778)2(31 cm) = 2800 cm/s2
4a. 1.7 Hz
amax(vertical) = 0.17 m/s2
amax = (2πf)2A
A = amax = 0.17 m/s2 = 0.17 m/s2 = 1.49 x 10-3 m or 0.149 cm
(2πf)2 (10.681415)2 114.092626
b. vmax = 2πfA
= 2π(1.7 Hz)(1.49 x 10-3 m) = 1.6 x 10-2 m/s
,5a. f = 1/T = 1/0.04 s = 25 Hz
A = 0.04 m
amax = (2πf)2A = (2π(25 Hz))(0.04 m) = 990 m/s2
b. 1 m/s2 = 0.101971621 g
990 m/s2 0.101971621 g = 100 g
1 m/s2
6.
5.9 cm ?
1.3 kg 2.0 kg
F = -kx
F = mg
k = spring constant
x = stretch of spring
(1.3 kg)(9.81 m/s2) = K 5.9 cm
100 cm/m
12.753 = -K(0.059)
K = -216.15254
(2.0 kg)(9.81 m/s2) = -216.15254(x)
19.62 = -216.15254(x)
x = 9.08 cm
, 7a. 84 bpm
f = 84/60 = 1.4 Hz
b. T = 1/1.4 Hz = 0.71 s
8a. 0.700 kg
Spring constant = 18 N/m
Speed = 43 cm/s
KE = PE
mv2 = kA2
(0.700 kg)(0.43 m/s)2 = (18 N/m)(A)2
0.12943 = (18 N/m)(A)2
A2 = 0.007190556
A = 0.085 m or 8.5 cm
b. T = 2π√m/K
= 2π 0.700 kg = 1.2390608 s
18 N/m
v = (2π/t)[√(A2 – x2)] x = 0.35A A = 8.5 cm
= 2π {√8.5 cm2 – [(0.35)(8.5)]2}
1.2390608 s
= 5.0709257 s[√(72.25 – 8.850625)]
= (5.0709257 s)(7.962372) = 40 cm/s
