### Understanding the Oscillation Amplitude of a Damped Harmonic Oscillator**Concept Overview**: A lightly damped harmonic oscillator, with a natural (undamped) angular frequency \( \omega_0 \), is being driven by an external force at a different angular frequency \( \omega_d \). The problem is to determine which of the provided traces in the graph best represents the relationship between driving frequency \( \omega_d / \omega_0 \) and oscillation amplitude \( A / A_0 \).**Graph Analysis**:- **Axes**: - **X-axis**: Represents the normalized driving angular frequency, \( \omega_d / \omega_0 \). - **Y-axis**: Represents the normalized amplitude, \( A / A_0 \).- **Graph Traces**: - **A1 (Purple)**: Shows a peak around \( \omega_d / \omega_0 \approx 0.5 \) and quickly drops towards zero as \( \omega_d / \omega_0 \) increases. - **A2 (Green, dashed)**: Peaks sharply around \( \omega_d / \omega_0 \approx 1.5 \) and then declines. - **A3 (Cyan, dash-dot)**: Displays a wider peak around \( \omega_d / \omega_0 \approx 1 \) and decreases as \( \omega_d / \omega_0 \) increases. - **A4 (Orange, solid)**: Low and flat, with a minimal peak near \( \omega_d / \omega_0 \approx 0.5 \). - **A5 (Blue, dotted)**: Peaks notably around \( \omega_d / \omega_0 \approx 0.75 \), tapering off thereafter.**Question**: Which trace best matches the function of amplitude \( A(\omega_d / \omega_0) \) for this lightly damped oscillator? The solution would involve understanding resonance peaks typical in such oscillatory systems and selecting the appropriate trace based on the behavior described.**Answer Choices**:- O A1- O A2- O A3- O A4- O A5Use this graph to explore concepts such as resonant frequency and damping in oscillatory systems. The identified pattern helps in visualizing how amplitude varies with changing driving frequencies in practical applications.

Name: ### Understanding the Oscillation Amplitude of a Damped Harmonic Osci
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: ### Understanding the Oscillation Amplitude of a Damped Harmonic Oscillator**Concept Overview**: A lightly damped harmonic oscillator, with a natural (undamped) angular frequency \( \omega_0 \), is being driven by an external force at a different a

When the angular frequency is closest to (equal to) the driving frequency, the system reaches the resonance state. At this stage, it oscillates at the highest amplitude.So, when the angular frequency () is equal to the driving frequency (), the amplitude will be the highest. This characteristic can be seen in the plot of A3 because it has the highest amplitude.A3 is closest to A () behaviour of the oscillation amplitude vs the driving frequency.