Find velocity and acceleration using derivatives

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SUMMARY

The discussion focuses on finding velocity and acceleration in simple harmonic motion (SHM) defined by the equation x(t) = A cos(wt). Participants emphasize the importance of using derivatives to derive velocity as the first derivative, v(t) = -A w sin(wt), and acceleration as the second derivative, a(t) = -A w² cos(wt). The consensus is that the problem should remain in one dimension, as the position x is clearly defined in that context.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of derivatives in calculus
  • Familiarity with trigonometric functions
  • Basic concepts of velocity and acceleration
NEXT STEPS
  • Study the derivation of velocity and acceleration in simple harmonic motion
  • Learn about the applications of derivatives in physics
  • Explore the relationship between angular frequency (w) and SHM
  • Investigate the graphical representation of SHM and its derivatives
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for clear explanations of SHM concepts.

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Homework Statement


we know that the simple armonic motion is characterized by x(t)=Acos(wt), find velocity and acceleration of s.h.m. using derivatives.

Homework Equations

The Attempt at a Solution


i should find derivatives of the component of the vector R (Rcos(wt),Rsin(wt)).
 
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first derivative is velocity, second derivative is acceleration
 
I don't see why you would change this into a 2D problem. It is phrased as a 1D problem where x is position. Velocity should just be ##\frac{d}{dt} x(t) ##
 
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