Two simple pendulums A and B having lengths λ and λ /4 respectively are released from the position as shown in figure. Calculate the time after which the release of the two strings become parallel for the first time. Angle θ is very small.
Text Solution
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Sol.
The angular position of pendulum 1 and 2 are (taking angles to the right of reference line xx ′ to be positive)
θ 1 = θ cos 
[where T = 2 
]
θ 2 = – θ cos 
= cos 
For the strings to be parallel for the first time
θ 1 = θ 2
or cos 
= cos 
∴ 
t = 2n 
± 
for n = 0, t = 
for n = 1, t = 
, 
∴ Both the pendulum are parallel to each other for the first time after t = 
= 
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