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?

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? <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/eb839fd493ce02bb27f9ed0aacb3ae32-.png" /> (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

Tardigrade Admin · Accepted Answer

In SHM, v2=ω2(A2-y2) and a2=ω4 y2 Hence, v2=ω2 A2-(a2 / ω2) or v2+((a2/ω2))=ω2 A2

Q. 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?

1, 2 and 3 are correct

1 and 2 are correct

2 and 4 are correct

1 and 3 are correct

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

Q. 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?

1, 2 and 3 are correct

1 and 2 are correct

2 and 4 are correct

1 and 3 are correct

In SHM, v2=ω2(A2−y2) and a2=ω4y2 Hence, v2=ω2A2−(a2/ω2) or v2+(ω2a2​)=ω2A2

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