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**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**

see attachment for rest of equations

_{m}[tex]\dot{x}[/tex]+kx=F_{o}sin[tex]\omega[/tex]tsee attachment for rest of equations

**3. m= 0.5 kg, s=100N/m, R**

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.

_{m}=1.4 kg/s, F_{o}=2NSo 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.