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Standard XII

Physics

Time Period Independent of Amplitude

A particle mo...

Question

A particle moves so that its acceleration a is given by $a = b n$ , where x is displacement from equilibrium position and b is non negative real constant. The time period of oscillation of the particle is :

2 π \sqrt{b}

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\frac{2 π}{\sqrt{b}}

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\frac{2 π}{b}

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2 \sqrt{\frac{π}{b}}

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Solution

The correct option is B $\frac{2 π}{\sqrt{b}}$
We have $a = - b x$
For simple harmonic motion
Or comparing $ω^{2} = b$
$ω = \sqrt{b}$
$\frac{2 π}{t} = \sqrt{b}$
or $t = \frac{2 π}{\sqrt{b}}$

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A particle moves so that its acceleration a is given by a=bn, where x is displacement from equilibrium position and b is non negative real constant. The time period of oscillation of the particle is :

The correct option is B 2π√bWe have a=−bxFor simple harmonic motionOr comparing ω2=bω=√b2πt=√bor t=2π√b

A particle moves so that its acceleration a is given by $a = b n$ , where x is displacement from equilibrium position and b is non negative real constant. The time period of oscillation of the particle is :

The correct option is B $\frac{2 π}{\sqrt{b}}$
We have $a = - b x$
For simple harmonic motion
Or comparing $ω^{2} = b$
$ω = \sqrt{b}$
$\frac{2 π}{t} = \sqrt{b}$
or $t = \frac{2 π}{\sqrt{b}}$