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.)

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

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:

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

When t = 1/4 s

When t = 1/2

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm