A particle SHM and its position varies with time as x- A sin - t- Its average speed during its motion from mean position to mid-point of mean and extreme position is-

The correct option is B 3Aωπ x=A2=Asinω t sinω t=12 ω t=π6 ⇒ t=π6ω Average speed =Total distanceTotal time A/2π/6ω =6Aω2 ...

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Standard XII

Physics

Relating Circular Motion to SHM

A particle SH...

Question

A particle SHM 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:

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\frac{3 A ω}{π}

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\frac{A ω}{2 π}

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\frac{2 A ω}{π}

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Solution

The correct option is B $\frac{3 A ω}{π}$
$x = \frac{A}{2} = A sin ω t$
$sin ω t = \frac{1}{2}$
$ω t = \frac{π}{6}$
$\Rightarrow t = \frac{π}{6 ω}$
Average speed $= \frac{T o t a l d i s t a n c e}{T o t a l t i m e}$
$\frac{A / 2}{π / 6 ω}$
$= \frac{6 A ω}{2 π}$
$∴$ Average speed $= \frac{3 A ω}{π}$ .

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A particle SHM and its position varies with time as x= A sin ωt. Its average speed during its motion from mean position to mid-point of mean and extreme position is:

The correct option is B 3Aωπx=A2=Asinωtsinωt=12ωt=π6⇒t=π6ωAverage speed=TotaldistanceTotaltimeA/2π/6ω=6Aω2π∴ Average speed=3Aωπ.

A particle SHM 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: