Question

An instantaneous displacement of a simple harmonic oscillator is x = A cos (wt + π/4). Its speed will be maximum at time(a) π/4ω(b) π/2ω(c) π/ω(d) 2π/ω

Answer 1

this is the answer hope it helps

Answer 2

Answer:

A) π/4

Explanation:

Instantaneous displacement of a simple harmonic oscillator is x = A cos (wt + π/4

Where, π/4 is initial phase only.

The time interval between zero velocity and half the maximum velocity will be calculated.The velocity is the time derivative of displacement:

v = dy/dt = -Aω(sin ωt + π/4).

Its maximum magnitude equal to Aω  is obtained when ωt = π/4, from which t = π/4ω.

So after time interval of  π/4w the velocity will drop from maximum velocity to half of the maximum velocity.