Simple Harmonic Motion Maxiumum Velocity

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SUMMARY

The discussion focuses on calculating the maximum velocity and maximum acceleration of a mass-spring system undergoing simple harmonic motion (SHM). Given a time period of 0.25 seconds and an amplitude of 30 mm, the maximum speed is derived using the formula ds/dt = A * 2πf * cos(2πft), where the maximum speed occurs when cos(2πft) equals 1. The frequency is calculated as f = 1/T, resulting in a maximum speed of 3.77 cm/s and a maximum acceleration of 14.92 m/s².

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with the concepts of amplitude and time period
  • Knowledge of trigonometric functions in physics
  • Ability to perform calculations involving frequency and velocity
NEXT STEPS
  • Study the derivation of the equations of motion for simple harmonic oscillators
  • Learn about the relationship between amplitude, frequency, and maximum speed in SHM
  • Explore the concept of maximum acceleration in oscillatory motion
  • Investigate real-world applications of simple harmonic motion in engineering
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Physics students, mechanical engineers, and anyone interested in the principles of oscillatory motion and its applications in real-world systems.

richardstan
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Hi, wondering if someone could help me with the following question.

A mass is hung from the lower end of a light vertical spring, whose upper end is fixed. The mass is pulled down and released and the time period of the oscillating system is measured. If the time period is 0.25s and the amplitude of oscillation is 30mm, calculate:

i.)the maximum speed
ii.)the maxiumum acceleration

I have an equation for the speed:

ds/dt = A 2(pi)f cos(2(Pi)ft)

i have a value for the frequency, is the maximum speed when the value of cos(2(Pi)ft) = 1?
Thanks
Richard.
 
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