Example 17: A pendulum of length t hangs against a wall inclined at an angle 0 to the horizontal. Show that the time of complete oscillation is 2% gsin

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Example 17: A pendulum of length t hangs against a wall inclined at an angle e to the
horizontal. Show that the time of complete oscillation is 2%
gsine
Solution: Let a bob of mass m be at a position P from pgsition C on the vertical line OC such
that ZPOC = 0. where OC is the line of greatest slop through O.
From the Fig 4.11 (a) it is clear that the component of the weight along the plane is mg sine
and hence the equation of motion of the bob along the tangent at Pis
mg
(mg sin 8)
(b)
-----
mg sin e
(a)
Fig. 10.11
=-(mgsine)sino or
d ((0)
df
-gsinef-
dt
or
=-gsine . (In case, when o is very small)
or
df
sine p=0
d u'o =0. where u= sine
df
Thus, the motion of the bob is simple harmonic with time period of oscillation as
=2n
Vgsine
Transcribed Image Text:Example 17: A pendulum of length t hangs against a wall inclined at an angle e to the horizontal. Show that the time of complete oscillation is 2% gsine Solution: Let a bob of mass m be at a position P from pgsition C on the vertical line OC such that ZPOC = 0. where OC is the line of greatest slop through O. From the Fig 4.11 (a) it is clear that the component of the weight along the plane is mg sine and hence the equation of motion of the bob along the tangent at Pis mg (mg sin 8) (b) ----- mg sin e (a) Fig. 10.11 =-(mgsine)sino or d ((0) df -gsinef- dt or =-gsine . (In case, when o is very small) or df sine p=0 d u'o =0. where u= sine df Thus, the motion of the bob is simple harmonic with time period of oscillation as =2n Vgsine
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