Simple harmonic motion question

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SUMMARY

The discussion focuses on calculating the time taken for an object undergoing Simple Harmonic Motion (SHM) with a period of 0.9 seconds and an amplitude of 0.32 meters. The object starts at its maximum displacement of 0.32 m and is at rest at t=0. The time to move from 0.32 m to 0.16 m is calculated as 0.15 seconds, while the time to move from 0.16 m to 0 is determined by taking one-quarter of the period (0.9s/4), resulting in 0.225 seconds. The calculations utilize the equations x=Asin(wt) and x=Acos(wt), confirming the correct approach to solving the problem.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with trigonometric functions in physics
  • Knowledge of angular frequency and its calculation
  • Ability to manipulate equations involving sine and cosine functions
NEXT STEPS
  • Study the derivation of the equations for SHM, specifically x=Asin(wt) and x=Acos(wt)
  • Learn about angular frequency and its role in SHM calculations
  • Explore the concept of phase shifts in SHM
  • Practice solving SHM problems with varying amplitudes and periods
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Students studying physics, particularly those focusing on mechanics and oscillations, as well as educators looking to enhance their understanding of Simple Harmonic Motion calculations.

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Homework Statement



An object undergoing SHM with a period 0.9s and amplitude of 0.32 m at t=0 the object is at 0.32 m and is instantaneously at rest. Calculate the time it takes the object to go a) from 0.32 to 0.16 m
b) from 0.16 m to 0

i can do a but don't understand why when i do the calculation x is not -1/2 and is 1/2

Homework Equations


x=Asin(wt)




The Attempt at a Solution



so for first part 1/2 = 0.32 cos (2+2/9)*pi * t

i get 0.15 correct answer and for part b i do the same thing because it is the same distance excpt i shift the graph so t1 is at 0.16 like this 0.16 = a cos ((wt) - pi/4)
 
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If 0.15s is the correct value for the time to reach 0.16m from 0.32m, then to reach 0 from 0.32m is the time for exactly one quarter of a period. (=0.9s/4)
The time from 0.16m to zero is then just the time for the quarter period minus your first answer.
 

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