If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

• a²T²+ 4π²v²

• aT/x

• aT + 2πv

• aT/v 

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance.Then 

• 18 > x

• x >54

• 54 > x > 36 

• 36 > x > 18

B.

x >54

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

• 0.5 s

• 0.75 s

• 0.125 s

• 0.325 s

A point mass oscillates along the x-axis according to the law x = x₀ cos (ωt - π/4). If the acceleration of the particle is written as a = A cos (ωt + δ), then

• A = x₀ , δ = – π/4

• A = x₀ ω₂ , δ = π/4 

• A = x₀ ω₂, δ = –π/4 

• A = x₀ ω2, δ = 3π/4

D.

A = x₀ ω2, δ = 3π/4