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) = (1/4)e^-t cos6t, where y is the displacement in feet and t is the time in seconds. Find the displacement when t is equal to 0.
Would this be 1/4?
anything^0 = 1
cos 0 = 1
so
(1/4) (1)(1) = 1/4
To find the displacement when t is equal to 0, we substitute t = 0 into the given equation y(t) = (1/4)e^-t cos6t.
Substituting t = 0 into the equation, we have:
y(0) = (1/4)e^0 cos6(0)
= (1/4)(1)(1)
= 1/4
Therefore, the displacement when t is equal to 0 is indeed 1/4.