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A particle is performing a linear simple harmonic motion. If the instantaneous acceleration and velocity of the particle are a and v respectively, identify the graph which correctly represents the relation between a and v

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a

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b

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c

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d

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answer is C.

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Detailed Solution

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$\begin{array}{l} a = - ω^{2} x \\ x = - \frac{a}{ω^{2}} \\ V = ω \sqrt{A^{2} - x^{2}} \\ V^{2} = ω^{2} A^{2} - ω^{2} x^{2} \\ V^{2} = ω^{2} A^{2} - ω^{2} {(\frac{a}{ω^{2}})}^{2} \\ V^{2} = ω^{2} A^{2} - ω^{2} \frac{a^{2}}{ω^{4}} \\ V^{2} = ω^{2} A^{2} - \frac{a^{2}}{ω^{2}} \\ V^{2} = - \frac{1}{ω^{2}} (a^{2}) + ω^{2} A^{2} \\ y = - mx + c \end{array}$

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