Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A $2.00 kg$ object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression $F = 3.00 (s i n 2 π t)$ , where F is in Newton’s and t is in seconds. The force constant of the spring is $20.0 N m^{- 1}$ . Find
(a) The resonance angular frequency of the system,
(b) The angular frequency of the driven system, and
(c) The amplitude of the motion.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of the given data

The given data can be listed below as,

The external force equation is $F = 3.00 (\sin 2 π t)$ .
The mass of object is $m = 2.00 kg$ .

Step 2: Significance of the amplitude

Amplitude of driven oscillator with no damping is given by:

$A = \frac{\frac{F_{0}}{m}}{(ω^{2} - {ω_{0}}^{2})}$

Step 3: Determination of the amplitude of the motion.

Part (c):

We have to find the resonance angular frequency of the system:

By using concept and formula from step (1), we get

$A = \frac{\frac{F_{0}}{m}}{(ω^{2} - {ω_{0}}^{2})}$

Referring to subparts (a) and (b) of the SID: 947271-15-15.7-947271-15-53P-a and 947271-15-15.7-947271-15-53P-b

Substitute all the value in the above equation,

$A = \frac{\frac{(3 N m^{- 1})}{2 kg}}{\{{(6.28 s^{- 1})}^{2} - {(3.16 s^{- 1})}^{2}\}} A = 0.0509 m A = 5.09 cm$

Hence the amplitude of the motion is A = 5.09 cm.

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Identification of the given data

Step 2: Significance of the amplitude

Step 3: Determination of the amplitude of the motion.

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Identification of the given data

Step 2: Significance of the amplitude

Step 3: Determination of the amplitude of the motion.

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics