What is a conical pendulum? obtain an expression for its time period?

Question: What is a conical pendulum? obtain an expression for its time period?

A conical pendulum is a type of simple pendulum in which the bob or weight at the end of the string moves in a horizontal circle instead of a straight line. The string of the pendulum is attached to a fixed point at the top and makes a constant angle with the vertical axis. To obtain an expression for the time period of a conical pendulum, we use the formula for the time period of a simple pendulum and substitute the length of the string with L = r cosθ, where r is the radius of the circle and θ is the angle between the string and the vertical axis. By applying the equation of motion for circular motion, we get the formula T = 2π √(r/g) √tanθ, where T is the time period, r is the radius of the circle, g is the acceleration due to gravity, and θ is the angle of inclination. This formula shows that the time period of a conical pendulum depends on the radius of the circle and the angle of inclination, but is independent of the mass of the weight.

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