Respuesta :
Answer:
  v = 11.34 m / s
Explanation:
The simple harmonic motion of a spring and a mass is described by the equation
     x = A cos (wt + Фfi)
where A is the amplitude of movement in this case 0.25 m, w the angular velocity and fi the initial phase
the angular velocity is
      w = √ k / m
We can use Hooke's law to find the constant ka
      F = k x
where the force is 300N and the spring stretch is 0.25m
      k = F / x
      k = 300 / 0.25
      k = 1200 N / m
To find the phase angle di, let's use the system speed
     va = dx /dt
     va = A w sin (wt + Ф)
they tell us that the spring comes out of rest at time zero
     Vd = Aw sin Ф
the only way this term is zero is that the angle Ф = 0
substitutions in the first equations
     x = A cos wt
with
   w = √RA (1200 / 0.5)
   w = 48.99 rad / sec
we substitute in the first equations
    x = 0.25 cos (48.99 t)
speed is
     v = 0.25 48.99 without 48.99i
    Â
ask the speed for x = 0.15 m
we start by calculating the time it takes to get to this point
      x = A cos wt
      t = 1 / w cos-1 x / A
     we look for the time
      t = 1 / 48.99 cos-1 (0.15 / 0.25)
      t = 0.0189 s
this is the first time it takes to get to the requested point
  now we can calculate the speed
   v = Aw sin (wt)
     v = 0.25 48.99 sin (48.99 0.0189)
      v = 11.34 m / s
