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3.2 Principles of SHM
3.2 Principles of SHM
The variation of velocity with time = gradient of the displacement v time graph
3.2 Principles of SHM
The variation of velocity with time = gradient of the displacement v time graph
3.2 Principles of SHM
The variation of velocity with time = gradient of the displacement v time graph
x0
Displacement X:
X = x0 cos(w) t
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX =
dt
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX = - x0w sin(w) t
dt
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX = - x0w sin(w) t
dt
Acceleration a:
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX = - x0w sin(w) t
dt
Acceleration a:
d2X =
dt2
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX = - x0w sin(w) t
dt
Acceleration a:
d2X = - x0w2 cos(w) t
dt2
x0
Displacement X:
X = x0 cos(w) t
Velocity V:
dX = - x0w sin(w) t
dt
Acceleration a:
d2X = - x0w2 cos(w) t
dt2
acceleration
x0
x0
Conditions for SHM:
Acceleration is out of phase
with displacement by
1800 , π radians or T/2
acceleration
x0
x0
Conditions for SHM:
SHM occurs when the acceleration (hence force) is :
1. Proportional to displacement
2. Always in the opposite direction to the displacement
Acceleration is out of phase
with displacement by
1800 , π radians or T/2
acceleration
x0
Conditions for SHM:
SHM occurs when the acceleration (hence force) is :
1. Proportional to displacement
2. Always in the opposite direction to the displacement
Acceleration = - (constant)X X
Acceleration =
- (w)2
Acceleration =
- (2πf) 2 X X
Max Acceleration =
X
X
- (2πf) 2 X X Max
acceleration
x0
Conditions for SHM:
SHM occurs when the acceleration (hence force) is :
1. Proportional to displacement
2. Always in the opposite direction to the displacement
Acceleration = - (constant)X X
a =
- (w)2
a =
- (2πf) 2 X X
a Max =
X
X
- (2πf) 2 X X Max
acceleration
x0
Conditions for SHM:
SHM occurs when the acceleration (hence force) is :
1. Proportional to displacement
2. Always in the opposite direction to the displacement
Acceleration = - (constant)X X
a =
- (w)2
a =
- (2πf) 2 X X
a Max =
X
X
- (2πf) 2 X X Max
acceleration
x0
Conditions for SHM:
SHM occurs when the acceleration (hence force) is :
1. Proportional to displacement
2. Always in the opposite direction to the displacement
Acceleration = - (constant)X X
a =
- (w)2
a =
- (2πf) 2 X X
amax =
X
X
- (2πf) 2 X X Max
a   2 x
EQUATION OF SHM
Acceleration – Displacement graph
y m x
a
Gradient = - ω2
+A
x
-A
MAXIMUM ACCELERATION = ± ω2 A
= ( 2πf )2 A