Question

If a body is subjected to two mutually perpendicular SHM's given by equation x = a₁cosωt and y = a₂ sin (ωt + δ) which of the following is true?

• A. For δ = π/2, locus of body is circle.
• B. For δ = π/2 locus of body is ellipse
• C. For δ = π or δ = 0 locus is ellipse
• D. For δ = 0 locus is straight line.

Answer 1

Answer: (C)

For δ = π or δ = 0 locus is ellipse

Answer 2

x = a₁cosωt , y = a₂ sin (ωt + δ)

For δ = π/2

y = a₂ sin (ωt + π/2)

= a₂ cos ωt

⇒ x/a₁ = y/a₂

Equation of straight line (1) and (B ) is not applicable.

For δ = π or 0

y = − a₂ sin ωt

or a₂ sin ωt

⇒ $\frac{x^{2}}{a_{1}^{2}}$ + $\frac{y^{2}}{a_{2}^{2}}$ = 1

Equation of ellipse

∴ (3) is correct