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?
Increases by 2 times
Increases by 4 times
Remains the same
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.
