A 0.49-kg object connected to a light spring with a force constant of 21.2 N/m o

Question

A 0.49-kg object connected to a light spring with a force constant of 21.2 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest.

(a) Determine the maximum speed of the object.
_______________cm/s

(b) Determine the speed of the object when the spring is compressed 1.5 cm.
______________cm/s

(c) Determine the speed of the object when the spring is stretched 1.5 cm.
_____________cm/s

(d) For what value of x does the speed equal one-half the maximum speed?
_____________ cm

Explanation / Answer

(a)

= (k/m) = (21.2 / 0.49) = 6.57 rad/s

Maximum speed of the object

vmax = A= 6.57 * 4= 26.31 cm/s

(b)

Speed of the object v = [A^2 - x^2) = 6.57 [4^2 - 1.5 cm^2] = 24.36 cm/s

(c)

Speed of the object v = [A^2 - x^2) = 6.57 [4^2 - 1.5 cm^2] = 24.36 cm/s

(d)

v = ( 1/ 2) vmax = A / 2

  [ A 2 - x 2 ]= A/2

       [ A 2 - x 2 ] = A/ 2

             A 2 - x 2 = A 2 / 4

           3A 2 / 4 = x 2

                       x = 3.464 cm

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