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Q. 68

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 418

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Short Answer

An oscillator with a mass of and a period of has

an amplitude that decreases by during each complete oscillation.

If the initial amplitude is , what will be the amplitude

after oscillations?

The amplitude after oscillation is

See the step by step solution

Step by Step Solution

Step 1:  Concepts and principles

Damping oscillation: The mechanical energy in a real oscillating system decreases during oscillation because external forces, such as resistance, prevent the oscillation and convert the mechanical energy into thermal energy. The real oscillator and its movement are then said to be damped. If the damping force gives , where v is the speed of the oscillation and b is the damping constant, then the displacement of the oscillation is given by

where , the angular frequency of the damped oscillator can be given by

now is the angular frequency of an undamped oscillator

Step 2:  Given data

  • The mass of the oscillator can be:.
  • The time of the oscillator is: .
  • The amplitude of the oscillator decreases by during each complete oscillation.
  • The initial amplitude of the oscillator can be .

Step 3: Required data

The objective is to find out the amplitude of the oscillator after oscillations

Step 4:  solution

Since, The amplitude of the oscillation decreases by after a complete oscillation, the amplitude after the first oscillation is

where is the initial amplitude of the oscillation. The amplitude after second oscillation is

The amplitude of the oscillator after oscillations is

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