A470g block connected to a light spring for which the force constant is6.40N/m i

Question

A470g block connected to a light spring for which the force constant is6.40N/m is free to oscillate on a horizontal, frictionless surface. The block is displaced7.30cm from equilibrium and released from rest as in the figure.

(A) Find the period of its motion.

(B) Determine the maximum speed of the block.

(C) What is the maximum acceleration of the block?

(D) Express the position, velocity, and acceleration as functions of time.

Use the equations below. (Note that the direction is indicated by the sign in front of the equations.)

Explanation / Answer

D

a) for max value = cos (3.69 t + 0.16 ) = 1

3.69 t + 0.16 = 0 or 2

0 gives negative time ,

  3.69 t + 0.16 = 2

t = 1.659 s

b) for velcoity to be maximum:

sin ( 3.69t + 0.16) = 1

3.69t + 0.16 = /2

t = 0.382 s

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