Question

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by y(t) = 2e−t cos 4t, where y is the displacement (in centimeters) and t is the time (in seconds). Find the displacement when t = 0, t = 1 4 , and t = 1 2 . (Round your answers to two decimal places.)

Answer 1

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:

$y(t) = 2e^{-t} cos 4t$

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

$y(0) = 2e^{0} cos 4(0)\\y(0) = 2* 1*1\\y(0) = 2.00 cm$

When t = 1/4 s

$y(1/4) = 2e^{-1/4} cos 4(1/4)\\y(14) = 2e^{-1/4} cos (1)\\y(1/4) = 1.56 cm$

When t = 1/2

$y(1/2) = 2e^{-1/2} cos 4(1/2)\\y(14) = 2e^{-1/2} cos (2)\\y(1/2) = 1.21 cm$