Transcript Introduction to SHM (print version)

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.
Consider the forces acting on the mass when it is at rest.

FN

Fg
FN  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
or
  t
If the object starts at  o  0
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
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
xt   r cos t 
Amplitude (A) – the magnitude of
the maximum displacement
from the equilibrium position
xt   A cos t 
Simple harmonic motion is the projection of uniform circular motion on a diameter of the
circle in which the circular motion occurs
xt   A cos t 
  2 f
In rotation, ω refers to the
angular velocity.
xt   A cos2 f t 


t
For one complete oscillation
2

T
But
1
T
f
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