SHMMedium
Question
A ball is hung vertically by a thread of length ′l′ from a point ′P′ of an inclined wall that makes an angle ′α′ with the vertical. The thread with the ball is then deviated through a small angle ′b′ (β > α) and set free. Assuming the wall to be perfectly elastic, the period of such pendulum is/are
Options
A.
B.
C.
D.
Solution
maxm amplitude = βl
So time to travel angle a
x = x0 sin ωt
αl = βl sin ωt
t =
sin-1 
Now period of pendulum =
(actual time period) +2 (time to travel angle α)
=
=
Also if time taken to travel from right extreme position to wall is t then
− α = β cos ωt
⇒ cosωt = −
t =
T =
T =
So time to travel angle a
x = x0 sin ωt
αl = βl sin ωt
t =
sin-1 Now period of pendulum =
(actual time period) +2 (time to travel angle α)=
=
Also if time taken to travel from right extreme position to wall is t then
− α = β cos ωt
⇒ cosωt = −
t =
T =
T =
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