Question

Tell whether the function exhibits damped oscillation. If it does, identify the damping factor and tell whether the damping occurs as x→[infinity] or as x→0.

f(x)= π sin2πx

Answer 1

The function f(x) = π sin(2πx) exhibits damped oscillation with a damping factor of 2π, and damping occurs as x approaches infinity.

Step-by-step explanation:

The function f(x) = π sin(2πx) exhibits damped oscillation. To determine the damping factor, we need to examine the rate at which the amplitude of the oscillation decreases. In this case, the amplitude is given by the square of the sine function, so it decreases quadratically with increasing x. The damping occurs as x approaches infinity, as the amplitude approaches zero. Therefore, the damping factor is 2π.