1. Piston Problem
A piston moves a distance of 12cm from top to bottom (starts at top)
One complete piston movement takes 0.04 seconds.
The equation for the distance d = 6Cos(50πt) where t = time in seconds
And d is the vertical distance from point ‘P’ (cm)
During the first cycle how long is the piston less than 2cm above point ‘P’?
(Where point ‘P’ is the central position of the vertical movement)
Distance ‘d’
Point P
Method A
Method B
Method C
Review

2. Piston Problem method A
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Piston Problem method A
A piston moves a distance of 12cm from top to bottom (starts at top)
One complete piston movement takes 0.04 seconds.
Let A = 50πt
Solve 2 = 6Cos(50πt)
The equation for the distance d = 6Cos(50πt) where t = time in seconds
And d is the vertical distance from point ‘P’ (cm)
becomes 2 = 6Cos(A)
= Cos(A)
During the first cycle how long is the piston less than 2cm above point ‘P’?
(Where point ‘P’ is the central position of the vertical movement)
Distance ‘d’
A = Cos = 1.23
Other solution for A
Point P
OR A = 2π – 1.23 = 5.05
Use A to find ‘t’
As ‘t’ = A ÷ 50π
t =
t =
time difference
– =
sec

3. Piston Problem method B
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Piston Problem method B
A piston moves a distance of 12cm from top to bottom (starts at top)
One complete piston movement takes 0.04 seconds.
The equation for the distance d = 6Cos(50πt) where t = time in seconds
And d is the vertical distance from point ‘P’ (cm)
Solve 2 = 6Cos(50πt)
= Cos(50πt)
During the first cycle how long is the piston less than 2cm above point ‘P’?
(Where point ‘P’ is the central position of the vertical movement)
Distance ‘d’
(50πt) = Cos
50πt = 1.23
Point P
t =
OR 50πt = 5.05
t =
time difference
– =
t = sec

4. Piston Problem method C
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Piston Problem method C
A piston moves a distance of 12cm from top to bottom (starts at top)
One complete piston movement takes 0.04 seconds.
Solve 2 = 6Cos(50πt)
The equation for the distance d = 6Cos(50πt) where t = time in seconds
And d is the vertical distance from point ‘P’ (cm)
= Cos(50πt)
(50πt) = Cos
During the first cycle how long is the piston less than 2cm above point ‘P’?
(Where point ‘P’ is the central position of the vertical movement)
Distance ‘d’
50πt = 1.23
t =
Point P
Length of 1cycle?
50πt cycles = 2π
1 cycle = 2π ÷ 50π = 0.04
2nd time
0.04 – =
0.04
time difference
0.04 – =
sec

5. Piston Problem Review Home Solve 2 = 6Cos(50πt) Let A = 50πt
Simplify the equation 2 = 6Cos(A)
Solve 2 = 6Cos(50πt)
Rearrange to give ? = Cos(A)
becomes 2 = 6Cos(A)
= Cos(A)
Solve ? = Cos(A)
A = Cos = 1.23
Find other solutions for Solve A = ?
Other solution for A
Use each ‘A’ solution to find a value for t = ?
OR A = 2π – 1.23 = 5.05
Use A to find ‘t’
Answer Q time difference = ?
As ‘t’ = A ÷ 50π
t =
t =
time difference
– =
sec