A Simple harmonic oscillator has a period of $0.01 s$ and an amplitude of $0.2 m .$ The magnitude of the velocity in m $s e c^{- 1}$ at the mean position will be

20 π

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100

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40 π

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100 π

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Solution

The correct option is C $40 π$
Let equation of SHM is $x = A s i n (ω t)$ , Where $A = 0.2$ $m$ ,
$∴ v = A ω c o s (ω t)$ ,
$∴$ Velocity at mean position $v = A ω$
Given, Time Period $= 0.01 = \frac{2 π}{ω}$ $\Rightarrow ω = 200 π$
$∴$ Velocity $= 0.2 \times 200 π = 40 π$

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A Simple harmonic oscillator has a period of 0.01 s and an amplitude of 0.2m. The magnitude of the velocity in m sec−1 at the mean position will be

The correct option is C 40πLet equation of SHM is x=Asin(ωt), Where A=0.2 m,∴v=Aωcos(ωt), ∴ Velocity at mean position v=AωGiven, Time Period=0.01=2πω ⇒ω=200π∴ Velocity=0.2×200π=40π

A Simple harmonic oscillator has a period of $0.01 s$ and an amplitude of $0.2 m .$ The magnitude of the velocity in m $s e c^{- 1}$ at the mean position will be

The correct option is C $40 π$
Let equation of SHM is $x = A s i n (ω t)$ , Where $A = 0.2$ $m$ ,
$∴ v = A ω c o s (ω t)$ ,
$∴$ Velocity at mean position $v = A ω$
Given, Time Period $= 0.01 = \frac{2 π}{ω}$ $\Rightarrow ω = 200 π$
$∴$ Velocity $= 0.2 \times 200 π = 40 π$