the simple pendulum
DESCRIPTION
The simple pendulum. θ. L. m. The simple pendulum. θ. L. m. mg. The simple pendulum. θ. L. m. mg sin θ. mg. The simple pendulum. θ. L. x. m. mg sin θ. mg. Some trig: sin θ = x L - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/1.jpg)
The simple pendulum
L
m
θ
![Page 2: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/2.jpg)
The simple pendulum
L
m
θ
mg
![Page 3: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/3.jpg)
The simple pendulum
L
m
θ
mg
mg sinθ
![Page 4: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/4.jpg)
The simple pendulum
L
m
θ
mg
mg sinθ
x
![Page 5: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/5.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
![Page 6: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/6.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
+
![Page 7: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/7.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ+
![Page 8: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/8.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
+
![Page 9: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/9.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
+
![Page 10: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/10.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
From Newton’s second law F=ma
+
![Page 11: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/11.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
From Newton’s second law F=ma
ma = - mg x L
+
![Page 12: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/12.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
From Newton’s second law F=ma
ma = - mg x L
+
![Page 13: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/13.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
From Newton’s second law F=ma
and a = - g x L
+
![Page 14: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/14.jpg)
L
m
θ
mg
mg sinθ
x
Some trig: sin θ = x LFor small angles ( < 5 0) θ = x in radians L
Restoring force = - mg sinθ
( -ve sign indicates a left displacementand a right restoring force)
Restoring force = - mg x L
From Newton’s second law F=ma
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
+
![Page 15: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/15.jpg)
L
m
θ
mg
mg sinθ
x
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
+
![Page 16: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/16.jpg)
L
m
θ
mg
mg sinθ
x
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
- (2πf)2 = - g L
+
![Page 17: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/17.jpg)
L
m
θ
mg
mg sinθ
x
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
- (2πf)2 = - g L
f = 1 g 2π L
+
![Page 18: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/18.jpg)
L
m
θ
mg
mg sinθ
x
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
- (2πf)2 = - g L
f = 1 g 2π L
T = 2π L g
+
![Page 19: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/19.jpg)
L
m
θ
mg
mg sinθ
x
and a = - g x LCompare with SHM equation: a = - (2πf)2 x
- (2πf)2 = - g L
f = 1 g 2π L
T = 2π L g
+
Discuss:
effect of length,mass,
gravity,angle of swing.
![Page 20: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/20.jpg)
T = 2π L g
![Page 21: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/21.jpg)
Put in the form: y = m x + c
T = 2π L g
![Page 22: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/22.jpg)
Put in the form: y = m x + c
T 2 = 4 π 2 L + 0 g
T = 2π L g
![Page 23: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/23.jpg)
Put in the form: y = m x + c
T 2 = 4 π 2 L + 0 g
T 2
/s 2
L / m
T = 2π L g
![Page 24: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/24.jpg)
Put in the form: y = m x + c
T 2 = 4 π 2 L + 0 g
T 2
/s 2
Max force on pendulum bob occurs as it passes through the equilibrium:
T = 2π L g
L / m
m
mg
Ts
![Page 25: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/25.jpg)
Put in the form: y = m x + c
T 2 = 4 π 2 L + 0 g
T 2
/s 2
T = 2π L g
L / m
mv2 = Ts - mg r
m
mg
Ts
Max force on pendulum bob occurs as it passes through the equilibrium:
![Page 26: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/26.jpg)
Put in the form: y = m x + c
T 2 = 4 π 2 L + 0 g
T 2
/s 2
T = 2π L g
L / m
mv2 = Ts - mg but r = L so mv2 = Ts - mg r L
m
mg
Ts
Max force on pendulum bob occurs as it passes through the equilibrium:
![Page 27: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/27.jpg)
![Page 28: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/28.jpg)
![Page 29: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/29.jpg)
![Page 30: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/30.jpg)
![Page 31: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/31.jpg)
![Page 32: The simple pendulum](https://reader033.vdocuments.site/reader033/viewer/2022061610/56813d50550346895da70c8f/html5/thumbnails/32.jpg)