Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension in the string is mg cosθ
C. at the extreme positions
D. at the mean position
Tension in a string at any position is given as , where r is the length of pendulum and v is the instantaneous velocity of the bob. Now at the extremes points velocity of the bob is zero. Hence the term nullifies leaving alone . So, the tension in the string at extreme points is .
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The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.
(a) Show that the trajectory is an ellipse.
(b) Show that F = −mω2r
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