Consider a small spiracle body is attached at the lower end
of string whose upper end is fixed when a small spiracle body is moved in horizontal
circular the string attached to the body swipe over the surface of cone the whole
system is called conical pendulum.

### #EQUATION FOR TIME PERIOD FOR CONICAL PENDULUM

Consider a small spiracle body of mass m is moving in a horizontal
surface with angular velocity ω with
center at o. at any moment the body at ‘a’ the string attached to body moves an
angle θ with vertical the force are acting on the body are as
shown in figure.

### #VERTICAL COMPONENT

**Since there is no acceleration in the vertical direction, the vertical component of the tension in the string is equal and opposite to the weight**

T cosθ balance the weight ‘mg’ of body

T cos θ = mg ----------------------(1)

### #HORIZONTAL COMPONENT

T sin θ is acting
towards the center of the circular path. This component will provide circular
path.This component will provide the required centripetal force for circular
motion.

T sin θ= mrω

^{2}-----------------------(2)**Dividing equation (2)by equation (1)**

T sin θ/ T cos θ =
mr ω

^{2}/mg
Tan θ = r ω

^{2}/g
ω= √g Tan θ /r -------------------------(3)

If T

^{1}be the time period of revolution of the conical pendulum
T

^{1}= 2**π/**ω
T

^{1}= 2**π**√r/g Tan θ
T

^{1}= 2**π**√ L sin θ/ g sin θ/cos θ
T

^{1}= 2**π**√ L sin θ/ g
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