Explanation The amplitude of a forced harmonic motion is given by, A 0 = ( F 0 m ) ( ω 2 − ω 0 2 ) 2 + ( ω b m ) 2 Here, A 0 is the amplitude of forced harmonic motion, F 0 is the amplitude of the external force, m is the mass, ω is the applied frequency, ω 0 is the natural frequency and b is the damping constant. In order to calculate the maximum amplitude, differentiate the above equation with respect to ω and equate to zero. d A 0 d ω = 0 d d ω [ ( F 0 m ) ( ω 2 − ω 0 2 ) 2 + ( ω b m ) 2 ] = 0 ( F 0 m ) ( − 1 2 ) [ ( ω 2 − ω 0 2 ) 2 + ( ω b m ) 2 ] − ( 1 2 ) − 1 [ 2 ( ω 2 − ω 0 2 ) ( 2 �

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

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Chapter 14, Problem 64P

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The resonant amplitude peaks at ω=ω02−b22m2.

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Chapter 14, Problem 63P

Chapter 14, Problem 65P

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Chapter 14 Solutions

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Ch. 14.1 - An object is oscillating back and forth. Which of...Ch. 14.1 - A mass is oscillating on a frictionless surface at...Ch. 14.1 - If an oscillating mass has a frequency of 1.25 Hz,...Ch. 14.2 - Which of the following represents a simple...Ch. 14.2 - By how much should the mass on the end of a spring...Ch. 14.2 - The position of a SHO is given by x = (0.80 m)...Ch. 14.3 - Suppose the spring in Fig. 1410 is compressed to x...Ch. 14.5 - If a simple pendulum is taken from sea level to...Ch. 14.5 - Return to the Chapter-Opening Question, p. 369,...Ch. 14.5 - (a) Estimate the length of a simple pendulum that...

Ch. 14 - Give some examples of everyday vibrating objects....Ch. 14 - Is the acceleration of a simple harmonic...Ch. 14 - Explain why the motion of a piston in an...Ch. 14 - Real springs have mass. 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The resonant amplitude peaks at ω = ω 0 2 − b 2 2 m 2 .

Solution Summary: The author proves that the resonant amplitude peaks at omega =sqrt

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The resonant amplitude peaks at ω=ω02−b22m2.

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