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## Homework Statement

A 2.00 kg object on a horizontal frictionless surface is attached to a spring with

a spring constant 1000 N/m. The object is displaced from equilibrium 50.0 cm

horizontally and given an initial velocity of 4.0 m/s away from the equilibrium

position.

(a) What is the frequency of motion?

(b) What is the initial potential energy of the block-spring system?

(c) What is the initial kinetic energy?

(d) What is the amplitude of oscillation?

## Homework Equations

F = -kx

F = ma

[itex]\omega[/itex] = √(k/m)

T = 1/f

f = [itex]\omega[/itex]/2[itex]\pi[/itex]

PE = 0.5kx

^{2}

KE = 0.5mv

^{2}

## The Attempt at a Solution

(a) So I said:

T = 1/f → T = 2[itex]\pi[/itex]/f → T = 2[itex]\pi[/itex]√(m/k)

I subbed in my values and got T = 0.28s

Then I got f from f = 1/T and got f = 3.57s

^{-1}

(b) From PE = 0.5kx

^{2}I got PE = 125J

(c) From KE = 0.5mv

^{2}I got KE = 16J

(d) Its the amplitude part here that I got stuck. Could anyone clarify if my methods for the other parts were correct and point me some direction for part (d). Any help is much appreciated.

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