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) = yoe-at cos(wt) where yo = 0.75 m, a = 0.95s-1, and w= 6.3s-1. In order to find the vertical velocity of the car as a function of time we will need to evaluate the dy derivative of the vertical position with respect to time, or dt As a first step, which of the following is an appropriate way to express the function y(t) as a product of two functions?
a) y(t) = f(t) · g(t), where f(t) = yoe cos and g(t) wt.
b) y(t) = f(t) · g(t), where f(t) = yoe and g(t) = cos(wt).
c) y(t) = f(t)·g(t), where f(t) = yoe cos(wt) and g(t) = -at.
d) y(t) cannot be expressed as a product of two functions.

Answer 1

Answer:

The answer is "Option b"

Explanation:

$\to \bold{y(t) = y_0e^{-a t} cos(\omega t)}$

           $= y_0 e^{-\alpha t} cos(\omega t)$

and

$\bold{y(t) =f(t) \cdot g(t)}$

where  

$\to f(t) = y_{0}\ e^{- at} \ \ \ \ \ \\\\\ \to g(t) = cos {(\omega t)}$