Simple Harmonic Motion (SHM) - Notes - Class 11 PDF Download

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