LO 1

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Session
Simple Harmonic Motion - 1
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Session Objective
SHM - Concept Cause
Relationship between parameters motion
Displ. Vs Time relationship for SHM
SHM as a projection of circular motion
Energy of a SHM Oscillator
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Periodic and Oscillatory Motion
Periodic or harmonic motion motion which repeats
itself after regular interval.
Oscillatory or vibratory motion periodic motion
on same path (to and fro motion) between fixed
limits.
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Simple Harmonic Motion

• Oscillatory motion within fixed limits.

• Restoring force is always directed towards the
  mean position.

F -kx
or
a -?2x
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Measures of SHM
Amplitude (A) Maximum displacement from
equilibrium position.
Phase The argument of sine function in equation
of SHM is called phase.
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SHM and Circular Motion
x A sin?t
v A ? cos?t
a -A ?2 sin?t
As x A sin?t,
a -?2x
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Measures of SHM
Since,
F -kx
hence, ma -kx.
a -?2x
Also,
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Energy Variation in SHM
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Class Exercise - 1
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Solution
Let x A sin(wt q)
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Class Exercise - 2
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Solution
As total energy is constant so it oscillates with
time period infinity.
Hence answer is (a).
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Class Exercise - 3
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Solution
As force is directly proportional to X and
directed towards mean position (due to negative
sign of force), the particle will execute SHM.
The force constant of SHM would be K
(abc)2 So time period
Hence answer is (b).
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Class Exercise - 4
Amplitude of particle whose equation of motion is
represented as is (a) 5 (b) 4 (c) 3 (d)
Cannot solve
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Solution
Let A be the amplitude and f the initial phase,
then
Squaring and adding, we get
Hence answer is (a).
A2 25 or A 5
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Class Exercise - 5
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Solution
Dividing equation (ii) by equation (i), we get
Hence answer is (a).
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Class Exercise - 6
Phase difference between acceleration and
velocity of SHM is p. (True/False)
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Solution
So phase difference
So false.
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Class Exercise - 7
Keeping amplitude same if frequency of the source
is changed from f to 2f. Then total energy is
changed by (a) 3E (b) E (c) zero (d) 4E
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Solution
Hence answer is (a).
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Class Exercise - 8
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Solution
Hence answer is (a).
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Class Exercise - 9
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Solution
E µ A2
Hence (a) and (b) is appropriate graph.
Hence answer is (a, b).
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Class Exercise - 10
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Solution
PE KE
Hence answer is (a, b).
where A is amplitude of SHM.
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