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In a forced oscillation, if the amplitude is doubled while keeping the driving f

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Question: In a forced oscillation, if the amplitude is doubled while keeping the driving frequency constant, what happens to the energy of the system?

Options:

  1. Increases by 2 times
  2. Increases by 4 times
  3. Remains the same
  4. Decreases

Correct Answer: Increases by 4 times

Solution: 

Energy is proportional to the square of the amplitude, so if amplitude is doubled, energy increases by 2^2 = 4 times.

In a forced oscillation, if the amplitude is doubled while keeping the driving f

Practice Questions

Q1
In a forced oscillation, if the amplitude is doubled while keeping the driving frequency constant, what happens to the energy of the system?
  1. Increases by 2 times
  2. Increases by 4 times
  3. Remains the same
  4. Decreases

Questions & Step-by-Step Solutions

In a forced oscillation, if the amplitude is doubled while keeping the driving frequency constant, what happens to the energy of the system?
  • Step 1: Understand that in a forced oscillation, the system is being driven by an external force at a certain frequency.
  • Step 2: Know that the amplitude is the maximum extent of the oscillation from the rest position.
  • Step 3: Remember that energy in oscillating systems is related to the amplitude of the oscillation.
  • Step 4: Learn that energy is proportional to the square of the amplitude. This means if you double the amplitude, you calculate the new energy using the formula: Energy ∝ Amplitude^2.
  • Step 5: If the original amplitude is A, and it is doubled to 2A, the new energy becomes (2A)^2 = 4A^2.
  • Step 6: Compare the new energy (4A^2) to the original energy (A^2). The new energy is 4 times the original energy.
  • Step 7: Conclude that if the amplitude is doubled while keeping the driving frequency constant, the energy of the system increases by 4 times.
  • Energy in Oscillations – The energy of a system in forced oscillation is proportional to the square of the amplitude.
  • Forced Oscillation – A type of oscillation where an external force drives the system at a specific frequency.
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