A simple harmonic oscillation has an amplitude $A$ and time period $T$ . The time required to travel from $x = A$ to $x = \frac{A}{2}$ is :

\frac{T}{6}

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\frac{T}{4}

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\frac{T}{3}

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\frac{T}{12}

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Solution

The correct option is A $\frac{T}{6}$
In equation $x = A cos ω t$ , putting $x = \frac{A}{2}$ we get
$ω t = \frac{π}{3}$
$∴$ $(\frac{2 π}{T}) t = \frac{π}{3}$
or $t = \frac{T}{6}$

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A simple harmonic oscillation has an amplitude A and time period T. The time required to travel from x=A to x=A2 is :

The correct option is A T6In equation x=Acosωt, putting x=A2 we getωt=π3∴ (2πT)t=π3or t=T6

A simple harmonic oscillation has an amplitude $A$ and time period $T$ . The time required to travel from $x = A$ to $x = \frac{A}{2}$ is :

The correct option is A $\frac{T}{6}$
In equation $x = A cos ω t$ , putting $x = \frac{A}{2}$ we get
$ω t = \frac{π}{3}$
$∴$ $(\frac{2 π}{T}) t = \frac{π}{3}$
or $t = \frac{T}{6}$