Q

Give answer! - Oscillations and Waves - NEET

The oscillation of a body on a smooth horizontal surface is represented by the equation,

X = A cos ($\omega$ t)

where, X = displacement at time t

$\omega$ = frequency of oscillation

Which one of the following graphs shows correctly the variation of 'a' with 't'?

• Option 1)

• Option 2)

• Option 3)

• Option 4)

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As discussed

Composition of two SHM in perpendicular direction -

$x=A_{1}\sin \omega t$

$y=A_{2}\sin \left ( \omega t+\delta \right )$

- wherein

Resultant equation

$\frac{x^{2}}{A{_{1}}^{2}}+\frac{y{_{2}}^{2}}{A{_{2}}^{2}}-\frac{2xy\cos \delta }{A_{1}A_{2}}= \sin ^{2}\delta$

a=A coswt

v=-AwSinwt

a=$\frac{dv}{dt} = -Awd\frac{\left | Sincot \right |}{dt} = -Aw^{2}coscot$

$\therefore$ i.e the variation of a with and correctly shown by graph (3)

Option 1)

This option is incorrect

Option 2)

This option is incorrect

Option 3)

This option is correct

Option 4)

This option is incorrect

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