A16.6 kg object on a horizontal frictionless surface is attached to a spring with k = 2470 n/m. the object is displaced from equilibrium 28.1 cm horizontally and given an initial velocity of 12.6 m/s back toward the equilibrium position. what are (a) the motion's frequency, (b) the initial potential energy of the block-spring system, (c) the initial kinetic energy, and (d) the motion's amplitude?

To solve this problem it is necessary to apply the concepts related to Period in a spring, elastic potential energy and energy in simple harmonic movement.

From the definition we know that the period can be expressed as

Where

m= Mass

k = Spring constant

Our values are given as

m = 16.6Kg

K = 2470N/m

Therefore the period would be

PART A) The frequency is the inverse of the period therefore

PART B) Elastic potential energy depends on compression and elasticity therefore

PART C) Kinetic energy depends on mass and speed therefore

PART D) As energy is conserved, the total energy is equivalent to the dual ratio of the elasticity constant and the amplitude, mathematically,

Therefore the motion's amplitude is 1.07m

nah.   i'm just sleepy.