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Chapter 15: Q61P (page 439)

For Equationx=xmcos(蝇t+蠒), suppose the amplitudexmis given by

xm=Fm[m2(蝇d2鈭�蝇2)2+b2蝇d2]1/2

whereFmis the (constant) amplitude of the external oscillating force exerted on the spring by the rigid support in Figure below. At resonance,

  1. what is the amplitude of the oscillating object?
  2. what is the velocity amplitude of the oscillating object?

Short Answer

Expert verified
  1. The amplitude of oscillation at resonance,
    xm=Fmb蝇
  2. The velocity amplitude of oscillation at resonance,
    vm=Fmb

Step by step solution

01

Given

The amplitude is given as-

xm=Fm[m2(蝇d2鈭�蝇2)2+b2蝇d2]12

02

Understanding the concept

Use the condition of resonancefor damped oscillation in the given equation to get the required derivation for amplitude and velocity amplitude.

Formulae:

vm=蝇xm蝇d=蝇

03

(a) Calculate the amplitude of the oscillating object

The given equation of amplitude is

xm=Fm[m2(蝇d2鈭�蝇2)2+b2蝇d2]12

Also, the condition for resonance is

蝇d=蝇

Using this equation in the above equation of amplitude, we get

xm=Fm[0+b2蝇d2]12xm=Fmb蝇

04

(b) Calculate the velocity amplitude of the oscillating object

The equation for velocity amplitude is

vm=蝇xm

Hence,

vm=蝇脳Fmb蝇vm=Fmb

The velocity amplitude for the oscillating object is vm=Fmb.

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Most popular questions from this chapter

The vibration frequencies of atoms in solids at normal temperatures are of the order of1013Hz. Imagine the atoms to be connected to one another by springs. Suppose that a single silver atom in a solid vibrates with this frequency and that all the other atoms are at rest. Compute the effective spring constant. One mole of silver (6.021023atoms) has a mass of 108 g.

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