Q6. Consider a pendulum of constant length = OA and making a variable angle (t) with the vertical direction (see figure

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Q6 Consider A Pendulum Of Constant Length Oa And Making A Variable Angle T With The Vertical Direction See Figure 1 (62.27 KiB) Viewed 9 times

Q6. Consider a pendulum of constant length = OA and making a variable angle (t) with the vertical direction (see figure below). A mass m is attached to the pendulum at point A. 0 e(t) A 1) (a) Sketch the polar cylindrical system of coordinates attached to A and making a direct orthonormal basis {e} where r is the radial direction outwards from the origin O. (b) Derive the expression of the velocity and acceleration vectors in polar coordinates. [8 marks] 2) The forces exerted on the bob are the gravitational force E, and the tension force T. (a) Derive the components of the Newton's second law along the unit vectors e, and e (b) Along the differential equation is 0+ sin 0 = 0. Solve the equation considering the small angle approximation. [12 marks] [Total: 20 marks]