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the period of a simple pendulum is 2 s and the amplitude of vibration is 5 cm.write down the equation of its motion.what will be the displacement and velocity of particle after 1.5 s

the period of a simple pendulum is 2 s and the amplitude of vibration is 5 cm.write down the equation of its motion.what will be the displacement and velocity of particle after 1.5 s

Grade:12th Pass

1 Answers

Suresh Sonkar
42 Points
2 years ago
suppose particle starts from the mean position:
The equation of motion will be x = Asinωt
 
Where x is displacement at any time t and A is amplitude and ω is the angular velocity
 
Given time period T  = 2 sec
 
So                         ω  =  2π/T =  2π/2 = π
 
 Given amplitude   A  = 5 cm
 
So the equation of motion will be:
 
                                x  =  5sin(πt)…………………………(1)
 
Displacement at       t = 1.5 sec
             x  =  5sin(π(1.5)) = 5sin(1.5π)  = -5cm
at this point velocity of the particle : differentiation equation1 wrt to time ‘t’
                                v = 5*π cos(πt)  = 5*π cos(1.5π)  = 0
Means particle is at extreme position

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