Simple harmonic motion question

AI Thread Summary
The discussion revolves around calculating the time it takes for an object undergoing simple harmonic motion (SHM) to move between specific positions. The object has a period of 0.9 seconds and an amplitude of 0.32 meters, starting at rest at the maximum displacement. The first calculation correctly determines the time to move from 0.32 m to 0.16 m as 0.15 seconds. For the second part, the time to go from 0.16 m to 0 is derived by recognizing it takes a quarter of the period (0.225 seconds) and subtracting the time already calculated. The overall understanding hinges on the relationship between position, time, and the characteristics of SHM.
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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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