Question

Suppose the damping constant $b$of an oscillator increases.

A. Is the medium more resistive or less resistive?

B. Do the oscillations damp out more quickly or less quickly?

C. Is the time constant $\tau$increased or decreased?

Short answer

Because the time constant is inversely proportional to the damping constant, it can be deduced that as the damping constant increases, the "time constant" value $\tau$decreases.

Step-by-step solution

Introduction

The oscillation known as a damped oscillation is one that slows down and eventually ceases due to a resisting force.

The order of resistivity(part a)

(A)The damping constant reflects the order of resistivity; as the damping constant grows, so does the resistance.

Damped oscillation(part B)

(B) Because the medium's resistivity is high, it opposes the oscillations and dampens them out more quickly.

Time constant(part C)

(C)The expression for time constant is,

$\tau =\frac{m}{b}$

Here, $m$is mass and $b$is damping constant.

Because the time constant is inversely proportional to the damping constant,

"The passage of time remains constant" " $\tau$drops as the dissipation constant increases.