Question

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.

Answer 1

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