equilibrium position. x displacement equilibrium position x f displacement
TRANSCRIPT
![Page 1: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/1.jpg)
Equilibrium position
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Equilibrium position
xdisplacement
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Equilibrium position
x
F
displacement
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Equilibrium position
x
F
Resultant force or Restoring force
displacement
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Equilibrium position
x
F
Resultant force or Restoring force
displacement
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 6: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/6.jpg)
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 7: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/7.jpg)
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Effect on the time period of :1. increasing the mass2. using stiffer springs ?
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Mass on a spring
Equilibrium position
Downward displacement x
x
m
![Page 12: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/12.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F m
![Page 13: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/13.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
m
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Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM
m
![Page 15: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/15.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
m
![Page 16: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/16.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
m
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 17: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/17.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x
m
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 18: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/18.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x
ma = - k x
m
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 19: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/19.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x
ma = - k x
a = - k x m
m
If the resultant force is directed towards and proportional to the displacement from equilibrium,
then so is the acceleration,and the object executes SHM.
![Page 20: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/20.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
a = - k x m
m
![Page 21: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/21.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
Compare this with the SHM equation;
a = - k x m
m
![Page 22: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/22.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
a = - k x m
m
![Page 23: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/23.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
-k = - (2πf)2 m
a = - k x m
m
![Page 24: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/24.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
-k = - (2πf)2 m
k = 4 π 2 f 2 m
a = - k x m
m
![Page 25: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/25.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x - ve sign shows thatfor a downward displacement
there is an upward restoring force!
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
-k = - (2πf)2 m
k = 4 π 2 f 2 m
f = 1 k 2π m a = - k x
m
m
![Page 26: Equilibrium position. x displacement Equilibrium position x F displacement](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bff21a28abf838cbbf14/html5/thumbnails/26.jpg)
Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
-k = - (2πf)2 m
k = 4 π 2 f 2 m
f = 1 k 2π m a = - k x
m
m
T = 2π m k
or :
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Mass on a spring
Equilibrium position
Downward displacement x
x
Restoring force F
F
Laws used:Hooke’s law F = k ΔL
Newton’s 2nd F = ma
SHM a = -(2πf)2 x
When the mass is displaced a small distance xthe resultant upwards restoring force F:
F = - k x
ma = - k x
Compare this with the SHM equation;
a = - k x m
a = - (2πf)2 x
-k = - (2πf)2 m
k = 4 π 2 f 2 m
f = 1 k 2π m a = - k x
m
m
T = 2π m k
or :
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Mass on a spring
T = 2π m k
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
T 2 = 4 π 2 m + 0 k
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
T 2 = 4 π 2 m + 0 k
T 2
/s 2
m / kg
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
T 2 = 4 π 2 m + 0 k
T 2
/s 2
m / kg
Max spring tension = mg + kx
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
T 2 = 4 π 2 m + 0 k
T 2
/s 2
m / kg
Max spring tension = mg + kx
x = A ( amplitude )
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Mass on a spring
T = 2π m k
Put in the form: y = m x + c
T 2 = 4 π 2 m + 0 k
T 2
/s 2
m / kg
Max spring tension = mg + kx
Min spring tension = mg - kxx = A ( amplitude )
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