Simple harmonic motion and maximum speed

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SUMMARY

The maximum speed of an object undergoing simple harmonic motion (SHM) is determined by the equation v = -Aωsin(ωt), where A represents the amplitude and ω is the angular frequency. The maximum acceleration is given by a = -Aω²cos(ωt). The maximum acceleration occurs when cos(ωt) equals -1, resulting in a maximum value of Aω². Conversely, the maximum speed occurs when sin(ωt) equals -1, which can also be derived using conservation of energy principles.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of angular frequency (ω) and amplitude (A)
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Study the derivation of maximum speed in SHM using conservation of energy
  • Explore the implications of angular frequency on SHM behavior
  • Learn about the graphical representation of SHM and its velocity and acceleration functions
  • Investigate real-world applications of SHM in mechanical systems
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the principles of simple harmonic motion and its applications in real-world scenarios.

sauri
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I got a question, what is the maximum speed of an object undergoing SHM? and what is the max. acceleration.

I am not sure how to solve this without any data given. I know that velocity v=-Awsinwt. and acceleration is a=Awcoswt.
So how am I to find the max speed and max acceleration?. Pls help.
 
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sauri said:
I got a question, what is the maximum speed of an object undergoing SHM? and what is the max. acceleration.

I am not sure how to solve this without any data given. I know that velocity v=-Awsinwt. and acceleration is a=Awcoswt.
So how am I to find the max speed and max acceleration?. Pls help.

The max acceleration is - A \omega^2 cos (\omega t).

Well, what is the max acceleration you could get if you can use any time you want? That will be when the cos is equal to minus 1! (the max and min values of a cosine function are +1 or -1. Because of the overall minus sign, the acceleration will be maximum when the cosine function is minimum...which is when it is -1). When the sine is -1, what is the value of the acceleration? That's your answer.

The velocity will be max when the sine function is minimum...
 
Alternatively, to find the maximum speed, you can use conservation of energy.
 

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