Asinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. if the damping constant has a value b1, the amplitude is a1 when the driving angular frequency equals k/m√.

The new amplitude of the harmonic oscillator when the damping constant is  will be .

Further Explanation:

Given:

The amplitude of the harmonic oscillator is .

The damping constant of the spring is .

The angular frequency of operation of the harmonic oscillator is .

Concept:

The expression for the amplitude of a harmonic oscillator is given by:

Here, is the amplitude of the harmonic oscillator, is the maximum force, is the force constant of oscillator,   is the driving angular frequency and   is the damping constant of the oscillator.

The angular frequency of the harmonic oscillator is .

Substitute for ,   for and for in above expression.

Now, if the damping constant of the harmonic oscillator becomes .

Substitute for and for in above expression of amplitude.

Therefore, the new amplitude of the harmonic oscillator for the damping constant of is

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Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Oscillations

Keywords:  Harmonic oscillator, damping constant, force constant, A1, b1, 3b1, sinusoidally, varying driving force, amplitude, driving angular frequency.

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