Solving Mass on a Spring Homework: Step-by-Step Guide

[joeypeter]

Homework Statement

A 1.30 kg mass on a spring oscilates horizontally with little friction according to the following equation: x = 0.070cos(2.50t), where x is in meters and t in seconds.
1) Find the maximum energy stored in the spring during an oscillation.

2) Find the maximum velocity of the mass.

Homework Equations

I have no clue how to do this problem. Can someone show me step by step how to do it.

The Attempt at a Solution

 

[Snazzy]

The displacement function of simple harmonic motion is:

$$x(t) = Acos(\omega t +\phi )$$

There is an equation that relates the angular frequency to the mass and the spring constant, and the maximum energy of a SHM system is 1/2 kA^2.

The maximum velocity can be obtained by finding the derivative of the displacement function and determining what the maximum value of sin is.