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

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To solve the problem of a 1.30 kg mass oscillating on a spring, the maximum energy stored in the spring can be calculated using the formula 1/2 kA^2, where A is the amplitude of oscillation. The given displacement function is x = 0.070cos(2.50t), indicating an amplitude of 0.070 meters. The angular frequency can be derived from the equation, and the spring constant can be determined using the relationship between mass, angular frequency, and spring constant. The maximum velocity of the mass is found by taking the derivative of the displacement function and identifying the peak value of the sine function. This approach provides a clear step-by-step method to arrive at the required solutions.
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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

 
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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.
 

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