Equation for simple harmonic motion

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SUMMARY

The discussion centers on the equation for simple harmonic motion (SHM), specifically a damped oscillation equation presented as y=e^(-3wnt)*Asin(wdt)+(Asin(wt)/SQRT(l-(w^2/wn^2)^2). Participants clarify that this equation is not a standard SHM equation but rather a specific solution to a differential equation related to the vibration of a ball on a spring. The standard SHM equations provided include x(t) = A*cos(ωt + φ), v(t) = -Aω*sin(ωt + φ), and a(t) = -Aω²*cos(ωt + φ). To assist further, contributors request the original differential equation and initial conditions to reproduce the solution.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM) equations
  • Familiarity with differential equations and their solutions
  • Knowledge of damping functions in oscillatory systems
  • Experience with mathematical modeling software, such as Working Drawing
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  • Research the derivation of damped oscillation equations
  • Study the effects of initial conditions on differential equations
  • Explore the use of Excel for modeling physical systems
  • Learn about the role of driving functions in oscillatory motion
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Students in physics or engineering, particularly those working on assignments related to oscillatory motion and differential equations, as well as educators and professionals involved in mathematical modeling of physical systems.

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i was just wondering if anybody knew where i could find the equation for simple harmonic motion (SHM). I have found loads but not the right one. i need the one that starts... y=e(^-3wnt)*Asin(wdt)+(Asin(wt)/SQRT(l-(w^2/wn^2)^2+... anyone got any ideas? got assignment to hand into uni tomorrow and i need it bad :biggrin:
 
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:confused: I never saw any equation for SHM that starts like that. The ones I know are:
x(t) = A\cos (\omega t + \phi)
v(t) = -A\omega \sin (\omega t + \phi)
a(t) = -A\omega ^2 \cos (\omega t + \phi)
 
I looks to me like you have a specific solution to a specific problem. It appears to be a case of damped ossiliations, but in no way is it an equation that you will find on the web. If you could post the specifics of the problem it is a solution to we may be able to help you. We need the original DE and the initial conditions.
 
its an equation for the vibration of a ball on a spring, i am comparing my excel model to the one i made on a program called working drawing.
 
The equation you posted is the solution to a Differential Equation with initial values. Without this information, I do not see how we can reproduce the solution. What are the initial conditions, what is the damping function. (your solution is damped) Is there a driving function? Without these details we cannot reproduce the solution.
 
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