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Damped Harmonic Motion with a Sinusoidal Driving Force 
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#1
Jan2111, 04:18 PM

P: 194

1. An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the force and speed as a function of the driving frequency and find the frequencies for which the phase angle is 45°.
2. m[tex]\ddot{x}[/tex] +R_{m}[tex]\dot{x}[/tex]+kx=F_{o}sin[tex]\omega[/tex]t see attachment for rest of equations 3. m= 0.5 kg, s=100N/m, R_{m}=1.4 kg/s, F_{o}=2N So my first question is this, is omega the independent variable in this case? Meaning, I solve everything that I am able to and leave omega alone. Also, is the differential equation in #2 the right form? I am confused at how I obtain the equation of motion so that I can plot this. 


#2
Jan2111, 05:00 PM

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Yes, ω is the driving frequency, so it's the independent variable for what's being asked in the problem. I'm not sure what you mean by "leaving ω alone." You want to express the speed amplitude and the phase angle as a function of ω and the constant parameters of the system.
Yes, your differential equation is correct. It is the equation of motion for the system. Note that k is the spring constant, which you called also called s in the other equations. I think you have a typo in your equation for the phase angle. Also, what does c represent in that formula? 


#3
Jan2211, 03:05 PM

P: 194

The equation for the phase angle is wrong it should be tan[tex]^{1}[/tex](H)
where H=[tex]\frac{\omega*mk/\omega}{R_{m}}[/tex]. I'm still a little confused about what they are asking for in regards to plotting. 


#4
Jan2211, 10:40 PM

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Damped Harmonic Motion with a Sinusoidal Driving Force
By "speed amplitude," I assume the problem is asking for the amplitude of v(t). It will depend on ω.



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