DOC 57 .pdf - PHYSICS 203 initial displacement to be the...

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PHYSICS 203
d x
initial displacement to be the sum of the earlier displacements, viz.,
a
1
 a
2
, then according to
the superposition principle,, the displacement
x
3
 x
1
 x
2
x
3
after the same interval of time
t
will be
You can perform this activity by taking three identical simple pendulums. Release all three bobs
simultaneously such that their initial velocities are zero and initial displacements of the first,
second and the third pendulum are
a
1
,
a
2
and
a
1
 a
2
, respectively. You will find that at any
time the displacement
x
3
of the third pendulum will be the algebraic sum of the displacements of
the other two. In general, the initial velocities may be non-zero. Thus, the principle of
superposition can be stated as follows:
Superposition of Simple Harmonic Oscillations
When we superpose the initial conditions corresponding to velocities and amplitudes, the
resultant displacement of two (or more) harmonic displacements will be simply the algebraic sum