In this section, we study the effect of a fluid resistive force on oscillatory motion. We observe a horizontal block/spring system as shown in the simulation "The Damped Oscillator". Run the animation now. The block of mass m = 100 g is on a horizontal, frictionless surface. The block is connected to one end of a spring of spring constant k. The other end of the spring is fixed. The location of the block when in equilibrium is at x = 0. A vertical sail is connected to the block so that when the block moves, a damping force due to drag with the air acts on the block. In this section, we assume the block moves slowly enough that the fluid drag force is linearly proportional to the velocity and opposite in direction, as described by the mathematical expression Fa = - bu where the nonnegative constant b has units of N/(m/s), and the size of b depends on properties of both the sail and the fluid, which in this case is air.

In this section, we study the effect of a fluid resistive force on oscillatory motion. We observe a horizontal block/spring system as shown in the simulation "The Damped Oscillator". Run the animation now. The block of mass m = 100 g is on a horizontal, frictionless surface. The block is connected to one end of a spring of spring constant k. The other end of the spring is fixed. The location of the block when in equilibrium is at x = 0. A vertical sail is connected to the block so that when the block moves, a damping force due to drag with the air acts on the block. In this section, we assume the block moves slowly enough that the fluid drag force is linearly proportional to the velocity and opposite in direction, as described by the mathematical expression Fa = - bu where the nonnegative constant b has units of N/(m/s), and the size of b depends on properties of both the sail and the fluid, which in this case is air.

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Description: In this section, we study the effect of a fluid resistive force on oscillatory motion. We observe a horizontal block/spring system asshown in the simulation "The Damped Oscillator". Run the animation now. The block of mass m = 100 g is on a horizont

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

In this section, we study the effect of a fluid resistive force on oscillatory motion. We observe a horizontal block/spring system as
shown in the simulation "The Damped Oscillator". Run the animation now. The block of mass m = 100 g is on a horizontal,
frictionless surface. The block is connected to one end of a spring of spring constant k. The other end of the spring is fixed. The
location of the block when in equilibrium is at x 0. A vertical sail is connected to the block so that when the block moves, a damping
force due to drag with the air acts on the block. In this section, we assume the block moves slowly enough that the fluid drag force is
linearly proportional to the velocity and opposite in direction, as described by the mathematical expression
=
Ed
=
- bu
where the nonnegative constant b has units of N/(m/s), and the size of b depends on properties of both the sail and the fluid, which in
this case is air.

Reset the animation. Set the damping to zero, b = 0. Run the animation again. Use information in the plot of
x(t) to determine the spring constant k.
k = i
It is useful to define a new constant ß with SI units of radians per second, ß = b/(2m). What value of b corresponds to
BlwSHM
0.25? Things to note: (1) @SHM = √k/m is the angular frequency in the absence of damping; (2) you
found the value of k in question 1; (3) you are given that m = 100 g
b =
N/(m/s)
=
Using the expression x(t)
case where p/@SHM
x(t) =
= xmе-Bt
N/m
= 0.25.
cos (@'t + p)calculate the displacement x(t) of the oscillator at t = 2.50 sfor the
m

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