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

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SUMMARY

The discussion focuses on solving a physics homework problem involving a 1.30 kg mass oscillating on a spring, described by the equation x = 0.070cos(2.50t). The maximum energy stored in the spring is calculated using the formula 1/2 kA^2, where A is the amplitude of 0.070 m. The maximum velocity of the mass is determined by differentiating the displacement function and evaluating the maximum value of the sine function, leading to a clear understanding of simple harmonic motion (SHM).

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with the concepts of amplitude and angular frequency
  • Knowledge of calculus, specifically differentiation
  • Ability to apply energy equations in mechanical systems
NEXT STEPS
  • Study the derivation of the maximum energy formula for SHM systems
  • Learn how to differentiate trigonometric functions to find maximum values
  • Explore the relationship between mass, spring constant, and angular frequency
  • Investigate real-world applications of simple harmonic motion in engineering
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to reinforce concepts of simple harmonic motion.

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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:

[tex]x(t) = Acos(\omega t +\phi )[/tex]

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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