Simple Harmonic Motion: Determine Velocity at t=0.250s

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SUMMARY

The discussion focuses on calculating the velocity of a 39.8 g oscillating mass at t = 0.250 seconds using the equation x(t) = (2.00 cm)cos(5t - 4.00π). The correct formula for velocity is V_{x} = -ωA sin(ωt + φ), where ω = 5 rad/s and A = 2 cm. A common error identified was the use of incorrect units, specifically mixing meters per second with centimeters per second, which led to confusion in the calculations.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with trigonometric functions and their derivatives
  • Knowledge of unit conversions, particularly between centimeters and meters
  • Proficiency in using the formula for velocity in SHM: V_{x} = -ωA sin(ωt + φ)
NEXT STEPS
  • Review the principles of Simple Harmonic Motion and its equations
  • Practice unit conversions between different measurement systems
  • Explore the relationship between velocity and position in oscillatory motion
  • Learn about the implications of phase shifts in trigonometric functions
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of velocity calculations in Simple Harmonic Motion.

Moe*
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_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V_{x}= -\omegaAsin(\omegat + \phi)

The Attempt at a Solution



the attempt i just substitued
V_{x}= -5 rad/s*2sin( 5.00(0.250)-4\pi)... but this didn't work and i don't understand why?
 
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for the the equations posted its supposed to be V subscript x= wAsin(wt + phi) and x(t) = (2.00cm)cos(5t - 4pi)
 
Moe* said:
The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

What is the basic relation connecting velocity and position of any particle? Use that.
 
Moe* said:
_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V_{x}= -\omegaAsin(\omegat + \phi)

The Attempt at a Solution



the attempt i just substitued
V_{x}= -5 rad/s*2sin( 5.00(0.250)-4\pi)... but this didn't work and i don't understand why?
it seems work to me...
 
Your right it does work, i guess I entered in the wrong units when i answered the question( m/s instead of cm/s).
 

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