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Expert-verified Found in: Page 477 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # A ${\mathbf{2}}{\mathbf{.}}{\mathbf{00}}{\mathbf{ }}{\mathbf{\text{kg}}}$ object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression ${\mathbit{F}}{\mathbf{=}}{\mathbf{3}}{\mathbf{.}}{\mathbf{00}}\left(sin2\pi t\right)$, where F is in Newton’s and t is in seconds. The force constant of the spring is ${\mathbf{20}}{\mathbf{.}}{\mathbf{0}}{\mathbf{ }}{\mathbit{N}}{{\mathbit{m}}}^{\mathbf{-}\mathbf{1}}$. Find (a) The resonance angular frequency of the system, (b) The angular frequency of the driven system, and (c) The amplitude of the motion.

(c) The amplitude of the motion is A = 5.09 cm.

See the step by step solution

## Step 1: Identification of the given data

The given data can be listed below as,

• The external force equation is $F=3.00\left(\mathrm{sin}2\pi t\right)$.
• The mass of object is $m=2.00 \text{kg}$.

## Step 2: Significance of the amplitude

Amplitude of driven oscillator with no damping is given by:

${\mathbit{A}}{\mathbf{=}}\frac{\frac{{\mathbf{F}}_{\mathbf{0}}}{\mathbf{m}}}{\left({\omega }^{2}-{{\omega }_{0}}^{2}\right)}$

## 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

$A=\frac{\frac{{F}_{0}}{m}}{\left({\omega }^{2}-{{\omega }_{0}}^{2}\right)}$

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,

$A=\frac{\frac{\left(3 N{m}^{-1}\right)}{2 \text{kg}}}{\left\{{\left(6.28 {\text{s}}^{-1}\right)}^{2}-{\left(3.16 {\text{s}}^{-1}\right)}^{2}\right\}}\phantom{\rule{0ex}{0ex}}A=0.0509 \text{m}\phantom{\rule{0ex}{0ex}}A=5.09 \text{cm}$

Hence the amplitude of the motion is A = 5.09 cm. ### Want to see more solutions like these? 