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A 5.00-kg object oscillates on a spring with a force constant of 150 N/m. The damping coefficient is 0.200 kg/s. The system is driven by a sinusoidal force of maximum value 50.0 N, and an angular frequency of 20.0 rad/s. What is the amplitude A of the oscillations? A = If the driving angular frequency is varied, at what angular frequency o will resonance occur? rad/s

A 5.00-kg object oscillates on a spring with a force constant of 150 N/m. The damping coefficient is 0.200 kg/s. The system is driven by a sinusoidal force of maximum value 50.0 N, and an angular frequency of 20.0 rad/s. What is the amplitude A of the oscillations? A = If the driving angular frequency is varied, at what angular frequency o will resonance occur? rad/s

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**Harmonic Oscillator Problem** A 5.00-kg object oscillates on a spring with a force constant of 150 N/m. The damping coefficient is 0.200 kg/s. The system is driven by a sinusoidal force of maximum value 50.0 N, and an angular frequency of 20.0 rad/s. 1. **Question: What is the amplitude \(A\) of the oscillations?** - **Input Box**: \(A = \_\_\_\_) m 2. **Question: If the driving angular frequency is varied, at what angular frequency \(\omega\) will resonance occur?** - **Input Box**: \(\omega = \_\_\_\_) rad/s **Notes for Education:** - The problem involves a damped driven harmonic oscillator. - The parameters given allow for the calculation of amplitude using formulas involving mass, spring constant, damping coefficient, and driving frequency. - Resonance occurs when the driving frequency matches the natural frequency of the system, considering damping. - Ensure to use appropriate equations for damped and driven harmonic motion to solve the problems.
Transcribed Image Text:**Harmonic Oscillator Problem** A 5.00-kg object oscillates on a spring with a force constant of 150 N/m. The damping coefficient is 0.200 kg/s. The system is driven by a sinusoidal force of maximum value 50.0 N, and an angular frequency of 20.0 rad/s. 1. **Question: What is the amplitude \(A\) of the oscillations?** - **Input Box**: \(A = \_\_\_\_) m 2. **Question: If the driving angular frequency is varied, at what angular frequency \(\omega\) will resonance occur?** - **Input Box**: \(\omega = \_\_\_\_) rad/s **Notes for Education:** - The problem involves a damped driven harmonic oscillator. - The parameters given allow for the calculation of amplitude using formulas involving mass, spring constant, damping coefficient, and driving frequency. - Resonance occurs when the driving frequency matches the natural frequency of the system, considering damping. - Ensure to use appropriate equations for damped and driven harmonic motion to solve the problems.
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