Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A particle with a mass of $1.00 \times 10^{- 20} kg$ is oscillating with simple harmonic motion with a period of $1.00 \times 10^{- 5} s$ and a maximum speed of $1.00 \times 10^{3} m / s$ .
Calculate the angular frequency of the particle.
Calculate the maximum displacement of the particle.

The angular frequency of the particle is $6.28 \times 10^{5} rad / \sec$ .
The maximum displacement of the particle is $1.59 \times 10^{- 3} m$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Stating the given data

Mass of particle, $m = 1 \times 10^{- 20} kg$
Time period of SHM, data-custom-editor="chemistry" $t = 1 \times 10^{- 5} \sec$
Maximum speed of the body, $v = 1 \times 10^{3} m / s$

Step 2: Understanding the concept of motion

We can find the angular frequency by using the time period of motion. And maximum displacement can be found by using the formulae of maximum velocity and angular frequency.

Formula:

Angular frequency of a body in oscillation

$ω = \frac{2 π}{T}$ (i)

The velocity of a body undergoing simple harmonic motion

$v = {ωX}_{m}$ (ii)

Step 3: a) Calculation of angular frequency of the body

Using equation (i) and the given values, the angular frequency is given as follows:

$\begin{array}{rcl} ω & = & \frac{2 π}{1 \times 10^{- 5}} \\ = & 6.28 \times 10^{5} rad / \sec \end{array}$

Hence, the angular frequency is $6.28 \times 10^{5} rad / \sec$ .

Step 4: b) Calculation of maximum displacement

Using the given values and equation (ii), we get the maximum displacement as follows:

$1 \times 10^{3} = 6.28 \times 10^{5} \times X_{m} X_{m} = 1.59 \times 10^{- 3} m$

Hence, the maximum displacement is $1.59 \times 10^{- 3} m$ .

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Fundamentals Of Physics

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Short Answer

A particle with a mass of $1.00 \times 10^{- 20} kg$ is oscillating with simple harmonic motion with a period of $1.00 \times 10^{- 5} s$ and a maximum speed of $1.00 \times 10^{3} m / s$ .
Calculate the angular frequency of the particle.
Calculate the maximum displacement of the particle.

Step by Step Solution

Step 1: Stating the given data

Step 2: Understanding the concept of motion

Step 3: a) Calculation of angular frequency of the body

Step 4: b) Calculation of maximum displacement

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A particle with a mass of 1.00×10-20 kg is oscillating with simple harmonic motion with a period of 1.00×10-5 s and a maximum speed of 1.00×103 m/s. Calculate the angular frequency of the particle.Calculate the maximum displacement of the particle.

Step by Step Solution

Step 1: Stating the given data

Step 2: Understanding the concept of motion

Step 3: a) Calculation of angular frequency of the body

Step 4: b) Calculation of maximum displacement

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A particle with a mass of $1.00 \times 10^{- 20} kg$ is oscillating with simple harmonic motion with a period of $1.00 \times 10^{- 5} s$ and a maximum speed of $1.00 \times 10^{3} m / s$ .
Calculate the angular frequency of the particle.
Calculate the maximum displacement of the particle.