Oscillations
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Question : 17
Total: 25
A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
Solution:
When the car moves along a circular track, the bob of the simple pendulum will possess centripetal acceleration,
a c =
The acceleration due to gravity (g) acts vertically downwards.
Therefore, effective acceleration of the pendulum,
g ′ = √ g 2 + (
) 2
= √ g 2 + (
)
Hence, time period of the simple pendulum,
T = 2 π √
= 2 π √
The acceleration due to gravity (g) acts vertically downwards.
Therefore, effective acceleration of the pendulum,
Hence, time period of the simple pendulum,
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