A particle executes S.H.M. and its position varies with time as x=A sinω t Its average speed during its motion from mean position to mid-point of mean and extreme position is

Question

A particle executes S.H.M. and its position varies with time as x=A sinω t Its average speed during its motion from mean position to mid-point of mean and extreme position is (A) Zero (B) (3 A ω/π) (C) (A ω/2 π) (D) (2 A ω/π)

Tardigrade Admin · Accepted Answer

Phase at mean position =0 Phase at mid point (A/2)=A sin φ φ=(π/6) Time it takes to travel a phase difference of φ t=(2 π/ω) × (φ/2 π) or t=(φ/ω) or t=(π/6 ω) Average speed =( text Total distance / text Time taken ) =(A / 2/π / 6 ω) =(3 A ω/π)

Q. A particle executes S.H.M. and its position varies with time as $x = A sin ω t$ Its average speed during its motion from mean position to mid-point of mean and extreme position is

Zero

$\frac{3 A ω}{π}$

$\frac{A ω}{2 π}$

$\frac{2 A ω}{π}$

Q. A particle executes S.H.M. and its position varies with time as x=Asinωt Its average speed during its motion from mean position to mid-point of mean and extreme position is

Zero

π3Aω​

2πAω​

π2Aω​

Phase at mean position =0 Phase at mid point 2A​=Asinϕ ϕ=6π​ Time it takes to travel a phase difference of ϕ t=ω2π​×2πϕ​ or t=ωϕ​ or t=6ωπ​ Average speed = Time taken Total distance ​ =π/6ωA/2​ =π3Aω​

Q. A particle executes S.H.M. and its position varies with time as $x = A sin ω t$ Its average speed during its motion from mean position to mid-point of mean and extreme position is

$\frac{3 A ω}{π}$

$\frac{A ω}{2 π}$

$\frac{2 A ω}{π}$