Question

A particle is performing a linear simple harmonic motion. If the acceleration and the corresponding velocity of the particle are a and v respectively, which of the following graphs is/are correct?

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (A)

In SHM, $v^{2}=\omega^{2}\left(A^{2}-y^{2}\right)$
and $a^{2}=\omega^{4} y^{2}$
Hence, $v^{2}=\omega^{2} A^{2}-\left(a^{2} / \omega^{2}\right)$
or $v^{2}+\left(\frac{a^{2}}{\omega^{2}}\right)=\omega^{2} A^{2}$