Question

A mass of a spring vibrates in simple harmonic motion at a frequency of 8.0 Hz and an amplitude of 3.9 cm. If a timer is started with its displacement is a maximum, what is the speed of the mass when the timer reads 3 seconds

Answer 1

Answer:

 e = 50.27 give / s

Explanation:

The expression for simple harmonic motion is

    x = A cos (wt + Ф)

in this case they give us the amplitude A = 3.9 cm and frequency f = 8.0 Hz

The angular and linФear variables are related

      e = 2π d

      e = 2π 8

      e = 50.27 give / s

let's look for the constant fi

       so let's find the time to have the maximum displacement

       v = dx / dt

       v = -A w sin (wt +Ф)

for the point of maximum displacement the speed is I think

        0 = - sin (0 + Ф)

therefore fi = 0

Let's put together the equation of motion

          x = 0.039 sin (50.27 t)

          v = 0.039 50.27 sin (50.27 3)

           v = 1.96 50 0.01355

            v = 0.0266 m / s