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# Simple Harmonic Motion (SHM) - Notes Class 11 Notes | EduRev

## Class 11 : Simple Harmonic Motion (SHM) - Notes Class 11 Notes | EduRev

``` Page 1

Oscillatory Motion
? Object attached to a spring
? Simple harmonic motion
? Energy of a simple harmonic oscillator
? Simple harmonic motion and circular
motion
? The pendulum
Page 2

Oscillatory Motion
? Object attached to a spring
? Simple harmonic motion
? Energy of a simple harmonic oscillator
? Simple harmonic motion and circular
motion
? The pendulum
An Object Attached to a Spring
kx F
s
? ?
kx ma
x
? ?
x
m
k
a
x
? ?
When acceleration is proportional
to and in the opposite direction of
the displacement from equilibrium,
the object moves with Simple
Harmonic  Motion.
Page 3

Oscillatory Motion
? Object attached to a spring
? Simple harmonic motion
? Energy of a simple harmonic oscillator
? Simple harmonic motion and circular
motion
? The pendulum
An Object Attached to a Spring
kx F
s
? ?
kx ma
x
? ?
x
m
k
a
x
? ?
When acceleration is proportional
to and in the opposite direction of
the displacement from equilibrium,
the object moves with Simple
Harmonic  Motion.
Equation of Motion
x
m
k
dt
x d
a ? ? ?
2
2
? ? ? ? ? ? ? ? t A t x cos
Second order differential
equation for the motion of
the block
The harmonic solution for the spring-block system
m
k
? ?
where
Page 4

Oscillatory Motion
? Object attached to a spring
? Simple harmonic motion
? Energy of a simple harmonic oscillator
? Simple harmonic motion and circular
motion
? The pendulum
An Object Attached to a Spring
kx F
s
? ?
kx ma
x
? ?
x
m
k
a
x
? ?
When acceleration is proportional
to and in the opposite direction of
the displacement from equilibrium,
the object moves with Simple
Harmonic  Motion.
Equation of Motion
x
m
k
dt
x d
a ? ? ?
2
2
? ? ? ? ? ? ? ? t A t x cos
Second order differential
equation for the motion of
the block
The harmonic solution for the spring-block system
m
k
? ?
where
Some Terminology
? ? ? ? ? ? ? ? t A t x cos
Amplitude
Angular
frequency
Phase
constant
Phase
}
Page 5

Oscillatory Motion
? Object attached to a spring
? Simple harmonic motion
? Energy of a simple harmonic oscillator
? Simple harmonic motion and circular
motion
? The pendulum
An Object Attached to a Spring
kx F
s
? ?
kx ma
x
? ?
x
m
k
a
x
? ?
When acceleration is proportional
to and in the opposite direction of
the displacement from equilibrium,
the object moves with Simple
Harmonic  Motion.
Equation of Motion
x
m
k
dt
x d
a ? ? ?
2
2
? ? ? ? ? ? ? ? t A t x cos
Second order differential
equation for the motion of
the block
The harmonic solution for the spring-block system
m
k
? ?
where
Some Terminology
? ? ? ? ? ? ? ? t A t x cos
Amplitude
Angular
frequency
Phase
constant
Phase
}
Properties of Periodic Functions
? The function is
periodic with T.

? The maximum
value is the
amplitude.

?
Angular Frequency
?
? 2 1
? ?
f
T
Period
(s)
?
?
2
? f
Frequency
(1/s=Hz)
? / ?
? ? ? ? T t x t x ? ?
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