A simple pendulum of length I 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 ?
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Answer :
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Given:-
✦A simple pendulum of length I 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.
✦The pendulum makes small oscillations in a radial direction about its equilibrium position,
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To Prove:-
✦What will be its time period?..
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Solution:-
✦We know,
ar = v² / R
✦( ar - radial accleration )
✦( v - speed of the car on circular track )
✦( R - radius of the circular track )
➛Effective accleaccleration vector = - v² / R i - gj
➛Magnitude of effective acceleration = √ ( g² + v⁴ / R² )
We know,
➛=T = 2πr √(L / aeff)
➛=2πr √(L / √( g² + v⁴ / R² )
➛= 2πr √(L /( g² + v⁴ / R²)
➛The required time period is 2πr √(L /( g² + v⁴ / R²)
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