contestada

A 0.45 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by
x = (12 cm)cos[(17 rad/s)t + p/2 rad]
(a) What is the oscillation frequency (in Hz)? (b) What is the maximum speed acquired by the block? (c) At what value of x does this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what positive value of x does this occur? (f) What force, applied to the block by the spring, results in the given oscillation?
Give your answers in centimeter-based units, where applicable.

Respuesta :

(a) The angular frequency is  2.7 Hz

(b) The maximum speed is  2.04 m/s

(c) The maximum value is occur at mean position

 so the dispalcement is zero

(d) The maximum acceleration is 34.68 m/s^2.

(e) The acceleartion should be maximum at extrem positions

  so the position  x = A = 12 cm

( f )  The force on the block  15.6 N

Calculation :

The mass of the block m = 0.45 kg

The dispalcement of the block

 x = 12cm cos [(17 rad/s) t + (π/2 rad)]

 (a) The angular frequency

                 ω = 17 rad/s

                  2πf = 17 rad/s

then the frequency

               f = 17 / 2π = 2.7 Hz

(b) The maximum speed

           

              v max = Aω  = (12 cm) (17 rad/s)

                                 = 2.04 m/s

(c) The maximum value is occur at mean position

 so the dispalcement is zero

(d) The maximum acceleration

     a max  = Aω^2

                = (0.12 m) (17)^2 = 34.68 m/s^2

(e) The acceleartion should be maximum at extrem positions

  so the position  x = A = 12 cm

(f)  The force on the block

           F = ma = (0.45 kg) (34.68 )

                        = 15.6 N

Force or Energy Exercised or Applied: Cause of Movement or Change: Active Force. force of nature

Learn more about force here : https://brainly.com/question/12785175

#SPJ4

Otras preguntas