Oscillations
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Question : 11
Total: 25
Figures (a) and (b) correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.
Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.
Solution:
In figure (a) T = 2 s; A = 3 cm
At t = 0, OP makes angle
=
ϕ = +
x = A cos (
+ π ) = 3 cos (
+
)
orx = – 3 s i n π t
In figure (b) T = 4 s ; A = 2 m
At t = 0, OP makes an angle p with the positive direction of x-axis, i.e.ϕ = π ϕ = + π
Thus the x-projection of OP at time t will give us the equation of simple harmonic motion given by
x = A cos (
+ ϕ ) = 2 cos (
+ π ) = − 2 cos (
t )
(where x is in m)
At t = 0, OP makes angle
or
In figure (b) T = 4 s ; A = 2 m
At t = 0, OP makes an angle p with the positive direction of x-axis, i.e.
Thus the x-projection of OP at time t will give us the equation of simple harmonic motion given by
(where x is in m)
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