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Could you please help me determine if I've worked this problem out correctly.

1. Homework Statement

1. Homework Statement

A 2.86-kg object on a frictionless horizontal surface oscillates at the end of a spring with an amplitude of

7.81 cm. Its maximum acceleration is 3.74 m/s2.

Calculate the total mechanical energy.

## Homework Equations

1) Total Mechanical Energy: E = 0.5 k A^2

2) Spring Constant: k = m w^2 (where w = angular velocity)

3) Acceleration : a = -w^2 x

## The Attempt at a Solution

Given the Amplitude A, we must calculate the spring constant k to calc the total mechanical energy.

First find w using formula 3)

w = - sqr( a / x)

w = - sqr(3.74 / 0.0781)

w = - 6.92

Now substitute k in formula 1 with formula 2 to calculate the total mechanical energy.

E = 0.5 (m w^2) A^2

E= 0.5 (2.86) (-6.92)^2 (0.0781)^2

E= 0.0418 Joules