Transcript Simple Harmonic Motion

Oscillations – motions that repeat themselves
Period ( T ) – the time for one complete
oscillation
Frequency ( f ) – the number of oscillations
completed each unit of
time
Units: 1 Hertz (Hz) = 1 oscillation per second
1
T
f
Consider the forces acting on the mass when it is at rest.

Fs

Fg
Fs  Fg

Fnet  0
Equilibrium Position – Occurs when
the net force acting upon an
oscillating object is zero.
Net force acting on
a mass on a spring
Simple Harmonic Motion – the motion executed by a particle of mass m subject to a
force that is proportional to the displacement of the particle
but opposite in sign.


Fnet   x
Restoring Force – A force that acts towards the
equilibrium position and results in
oscillatory motion.


Fspring  kx
Hooke’s Law
Consider an object moving with uniform circular motion
In rotational terms, the
object moves with a
constant angular velocity ω
and therefore angular
position θ is given by
   t  o
Consider the projection of the motion of this object onto the horizontal plane.
This motion appears exactly like that
of a mass on the end of a spring!
Simple harmonic motion is the projection of uniform circular motion on a diameter of the
circle in which the circular motion occurs
x  r cos
r

r cos
But
   t  o
xt   r cos t  0 
Simple harmonic motion is the projection of uniform circular motion on a diameter of the
circle in which the circular motion occurs
xt   r cos t  0 
r

r cos
Amplitude (xm) – the magnitude of
the maximum displacement
from the equilibrium position
Phase Angle Phase Constant    the starting point of the oscillatory
motion, it depends on the displacement
of the object at t  0.


  0 when xo   xm
Oscillations
xt   xm cos t   
Simple Harmonic Motion – the motion executed by a particle of mass m subject to a
force that is proportional to the displacement of the particle
but opposite in sign.
– periodic motion in which the position is a sinusoidal
function of time
Mass on a spring
Oscillations
xt   xm cos t   
In rotation, ω refers to the angular velocity. However, in oscillatory motion, ω is called
Angular Frequency (ω) – rate of change of angular displacement of an oscillating object

x

t
For one complete oscillation
Angular Frequency
2

T
2

 2f
T
Units : rad
s