A simple pendulum, consists of an object suspended by a string. The object is as

Question

A simple pendulum, consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system oscillates by swinging back and forth in a vertical plane. If the string is 2.35 m long and makes an initial angle of 33.5° with the vertical, calculate the speed of the particle at the following positions.

(a) at the lowest point in its trajectory
(b) when the angle is 15.0°

Explanation / Answer

given: Length of the simple pendulum l = 2.35 m initial angel = 33.50 (a) v = sqrt [(2gl)(1-cos)]     = sqrt [2*(9.8 m/sec2)(2.35m)(1-cos(90-33.50))]     = 4.55 m/sec (b) v = sqrt [(2gl)(1-cos)]     = sqrt [2*(9.8 m/sec2)(2.35m)(1-cos(150))]     = 1.35 m/sec (a) v = sqrt [(2gl)(1-cos)]     = sqrt [2*(9.8 m/sec2)(2.35m)(1-cos(90-33.50))]     = 4.55 m/sec (b) v = sqrt [(2gl)(1-cos)]     = sqrt [2*(9.8 m/sec2)(2.35m)(1-cos(150))]     = 1.35 m/sec v = sqrt [(2gl)(1-cos)]     = sqrt [2*(9.8 m/sec2)(2.35m)(1-cos(150))]     = 1.35 m/sec

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