Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

What is the maximum acceleration of a platform that oscillates at amplitude 2.20 cm and frequency 6.60 Hz?

Maximum value of acceleration is 37.8 m/s².

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Stating the given data

Amplitude of platform oscillation, $x = 2.2 cm or 2.2 \times 10^{- 2} m^{2}$ .
Frequency of platform oscillation, $f = 6.60 Hz$ .

Step 2: Understanding the concept of acceleration

In a simple harmonic motion, the body undergoes acceleration for amplitude. Maximum acceleration occurs when the object is at end of its path. At those points, the force acting on the object is also maximum.

Formula:

The acceleration of a body in simple harmonic motion is directly proportional to the displacement, given by

$a_{m} = ω^{2} x$ (i)

Step 3: Calculation of acceleration of the body in motion

To find maximum acceleration, the angular frequency can be shown as follows:

$\begin{array}{rcl} ω & = & 2 πf \\ = & 2 π \times 6.60 (∵ f = 6.60 Hz) \\ = & 41.448 rad / \sec \end{array}$

Now using equation (i) and the given & derived values, the maximum acceleration is as follows:

$\begin{array}{rcl} a_{m} & = & 41 . 469^{2} \times 2.2 \times 10^{- 2} \\ = & 37.795 m / s^{2} \\ ≃ & 37.8 m / s^{2} \end{array}$

Hence, the value of maximum acceleration is $37.8 m / s^{2}$ .

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Fundamentals Of Physics

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Short Answer

What is the maximum acceleration of a platform that oscillates at amplitude 2.20 cm and frequency 6.60 Hz?

Step by Step Solution

Step 1: Stating the given data

Step 2: Understanding the concept of acceleration

Step 3: Calculation of acceleration of the body in motion

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Fundamentals Of Physics

Answers without the blur.

Short Answer

What is the maximum acceleration of a platform that oscillates at amplitude 2.20 cm and frequency 6.60 Hz?

Step by Step Solution

Step 1: Stating the given data

Step 2: Understanding the concept of acceleration

Step 3: Calculation of acceleration of the body in motion

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