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A simple pendulum is vibrating with an angular amplitude of 90 o as shown in the figure. For what value of x (angle between string and verticle) during its motion, the total acceleration is directed horizontally?

A simple pendulum is vibrating with an angular amplitude of 90o as shown in the figure. For what value of x (angle between string and verticle) during its motion, the total acceleration is directed horizontally?

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Grade:11

1 Answers

Arun
25750 Points
3 years ago
Acceleration of a simple pendulum is a=−ω 
2
 ×A×cos(ωt+θ), where ω is angular velocity, A is amplitude, t is time and θ is angle.
If θ is 0, then a=−ω 
2
 ×A×cos(ωt) so direction is vertically upwards, when θ is cos 
−1
 (1/3 
1/2
 ) then direction is horizontally, when θ is 90 
o
 , then a=ω 
2
 ×A×sin(ωt) so direction is vertically downwards.

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