SATHEE: Oscillations - Result Question 10

Oscillations - Result Question 10

13. The displacement of a particle along the $x$ -axis is given by $x = a \sin^{2} ω t$ . The motion of the particle corresponds to:

[2010]

(a) simple harmonic motion of frequency $ω / π$

(b) simple harmonic motion of frequency $3 ω / 2 π$

(d) simple harmonic motion of frequency $ω / 2 π$

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Answer:

Correct Answer: 13. (a)

Solution:

(a) $x = a \sin^{2} ω t = \frac{a}{2} (1 - \cos 2 ω t)$

$\frac{d x}{d t} = \frac{a}{2} 2 ω \sin 2 ω t$

$\Rightarrow \frac{d^{2} x}{d t^{2}} = \frac{4 ω^{2} a}{2} \cdot \cos 2 ω t$

This represents an S. H. M. of frequency

$= \frac{ω}{π}$

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Oscillations - Result Question 10

13. The displacement of a particle along the x-axis is given by x=asin2⁡ωt. The motion of the particle corresponds to:

Answer:

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13. The displacement of a particle along the $x$ -axis is given by $x = a \sin^{2} ω t$ . The motion of the particle corresponds to: