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A particle of mass point moves along the x-axis with displacement given by x = x0 cos(ωt − π/4). If its acceleration is expressed in the form a = A cos(ωt + δ), then
- A = x0ω², δ = 3π/4
- A = x0, δ = −π/4
- A = x0ω², δ = π/4
- A = x0ω², δ = −π/4
Correct answer: A = x0ω², δ = 3π/4
Solution
The acceleration of the particle can be derived from the displacement function by taking the second derivative with respect to time. This results in an expression that shows the amplitude as A = x0ω² and a phase shift of δ = 3π/4, indicating that the acceleration is out of phase with the displacement.
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