Simple Harmonic Motion - 3

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Session
Simple Harmonic Motion - 3
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Session Objective
Problems
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Class Exercise - 1
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Solution
Total time from A back to A is
20.67 0.47
2.28 s
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Class Exercise - 2
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Solution
In the figure, d and r are density of ball and
liquid respectively.
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Solution contd..
Compare this by equation a w2x
Also d 3r
T 1.1 s
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Class Exercise - 3
A block is resting on a piston which is moving
vertically with an SHM of period 1 s. At what
amplitude of motion will the block and piston
separate?
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Solution
For the block, mg R ma or R m(g a)
In order to separate the block, R 0 or a g
Now a w2x
Þ g w2x
0.248 m
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Class Exercise - 4
A plank with a body of mass m placed on it starts
moving straight up according to the law X a(1
coswt), where X is the displacement from the
initial position, w 11 s1. Find the time
dependence of the force that the body exerts on
the plank. If a 4.0 cm plot this dependence.
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Solution
Plot is shown in the figure.
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Class Exercise - 5
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Solution
Restoring force on the bob mg sin(q b)
Force on the bob mgsin(q b)
If q is small, b is also small.
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Solution contd..
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Class Exercise - 6
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Solution
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Solution contd..
Tension is also increased as shown below.
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Solution contd..
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Class Exercise - 7
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Solution
A displaced position of the rod through an angle
q is shown in the given figure. The displacement
of spring is x. Let K1 and K2 be the stiffness of
the springs respectively.
Considering the torques actingon the rod, we have
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Solution contd..
When q is small, cos q 1 and sin q q
Hence, the motion is SHM.
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Class Exercise - 8
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Solution
We will analyse the problem relative to the
rotating bar AB. As the acceleration of bar will
be centripetal, a pseudo force will act on the
sleeve away from centre and will be of magnitude
m w2x.
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Solution contd..
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Class Exercise - 9
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Solution
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Solution contd..
The force is provided by friction of thelower
block.
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Class Exercise - 10
A liquid of density d is kept in a vertical
U-tube of uniform cross section A. If the liquid
column is slightly depressed and left, show that
the resulting motion of the liquid is SHM and
find the period.
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Solution
Let the liquid be depressed by a height x in the
right side of the U-tube. Then the liquid rises
above on the left-side by a height x.
? Restoring force Pressure Area
(2xdg) A
or K 2dgA
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