Note that the correct times are t = 0, t = 1/4, t = 1/2. You can tell from the spaces between the two digits. i.e 1&4 and 1&2
Answer:
y(0) = 2.00 cm
y(1/4) = 1.56 cm
y(1/2) = 1.21 cm
Explanation:
This is a very simple exercise, the displacement of the oscillating weight from equilibrium has already been modeled by the equation:
[tex]y(t) = 2e^{-t} cos 4t[/tex]
Where y = displacement ( in cm)
and t = time (in seconds)
The task is to find the displacement when t = 0, 1/4 and 1/2
When t = 0 s
[tex]y(0) = 2e^{0} cos 4(0)\\y(0) = 2* 1*1\\y(0) = 2.00 cm[/tex]
When t = 1/4 s
[tex]y(1/4) = 2e^{-1/4} cos 4(1/4)\\y(14) = 2e^{-1/4} cos (1)\\y(1/4) = 1.56 cm[/tex]
When t = 1/2
[tex]y(1/2) = 2e^{-1/2} cos 4(1/2)\\y(14) = 2e^{-1/2} cos (2)\\y(1/2) = 1.21 cm[/tex]
