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Simple Harmonic Motion
Solution 2
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We are solving for the differnce in time between two points.
 
To do this we must first write an equation for the oscillation and then find the times at which the object is found at the two points.
 
What values do we have?
T = 4.0s
A = 10cm
 
We know that ω=2π/T, so substituting this into the equation for an oscillator:
 
y = Asin(2πt/T)
 
Now we can find at what times the oscillator is at the given points.
 
y = Asin(2πt/T)
0 = (10cm)sin(2π t /4)
sin(t*π/2)=0
t*π/2 = π
t = 0s
 
y = Asin(2πt/T)
6.0cm = (10cm)sin(2π t /4)
sin(t*π/2)=0.6
t*π/2 = sin-1(0.6)
t = 2sin-1(0.6) / π
  = 0.410s
 
t = 0.410s - 0.0s
 
 
= 0.410s

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Alesa Rabson & Maria Forero - Simple Harmonic Motion