Question

A design team for an electric car company finds that under some conditions the suspension system of the car performs in a way that produces unsatisfactory bouncing of the car. When they perform measurements of the vertical position of the car y

as a function of time t
under these conditions, they find that it is described by the relationship: y(t)=y0e−αtcos(ωt)
where y0=0.75m
, α=0.951/s
, and ω=6.3rad/s
. In order to find the vertical velocity of the car as a function of time we will need to evaluate the derivative of the vertical position with respect to time, or dydt
.

As a first step, which of the following is an appropriate way to express the function y(t)
as a product of two functions?

Answer 1

The function y(t) can be expressed as a product of two functions as follows:

y(t) = y0 * e^(-αt) * cos(ωt)

where y0 = 0.75 m, α = 0.951/s, and ω = 6.3 rad/s 1.

To find the vertical velocity of the car as a function of time, we need to evaluate the derivative of the vertical position with respect to time, or dy/dt. The derivative of y(t) with respect to t is given by:

dy/dt = -y0 * α * e^(-αt) * cos(ωt) - y0 * ω * e^(-αt) * sin(ωt)

Therefore, the vertical velocity of the car as a function of time is:

v(t) = dy/dt = -y0 * α * e^(-αt) * cos(ωt) - y0 * ω * e^(-αt) * sin(ωt)