A point mass oscillates along the x -axis according to the law x = x_0 (ω t - π/4) . If the acceleration of the particle is written as a = A (ω t + δ) - Physics MCQ AIEEE 2007 2026 | ExamTest.live

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A point mass oscillates along the x -axis according to the law x = x_{0} cos (ω t - π /4) . If the acceleration of the particle is written as a = A cos (ω t + δ), then:

Solution & Step-by-step Explanation

Given x = x_{0} cos (ω t - π /4) .Acceleration a = \frac{d ^{2} x}{d t ^{2}} .First derivative (velocity): v = \frac{d x}{d t} = - x_{0} ω sin (ω t - π /4) Second derivative (acceleration): a = \frac{d v}{d t} = - x_{0} ω^{2} cos (ω t - π /4) To express this in the form A cos (ω t + δ), we use the identity - cos θ = cos (θ + π) : a = x_{0} ω^{2} cos (ω t - π /4 + π) a = x_{0} ω^{2} cos (ω t + 3 π /4) Comparing with a = A cos (ω t + δ) : A = x_{0} ω^{2} and δ = 3 π /4

Try it yourself before checking the explanation above.

A point mass oscillates along the x -axis according to the law x = x_{0} cos (ω t - π /4) . If the acceleration of the particle is written as a = A cos (ω t + δ), then:

A = x_{0}, δ = - π /4

A = x_{0} ω^{2}, δ = - π /4

A = x_{0} ω^{2}, δ = π /4

A = x_{0} ω^{2}, δ = 3 π /4

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