Question

A particle executes shm and its position with time as x=asint. Its average speed during its motion from mean position to mid-point of mean and extreme position is

Answer 1

total distance = A/2

total time = t (suppose)

then, A/2 = A sin wt

A/2 = A sin (2pi/T)t           {because w= 2pi/T}

1/2 = sin (2pi/T)t

sin(pi/6) =sin(2pi/T)t

pi/6 = (2pi/T)t

t= T/12

avg. speed = total distance / total time

v = (A/2)/(T/6)

v= 3A/T

v= 3A/(2pi/w)

v= 3Aw/2pi