Amplitude of Sinusoidal Motion for 0.269 kg Mass on 80.3 N/m Spring

[bebop721]

An object with mass 0.269 kg is hung on a spring whose spring constant is 80.3 N/m. The object is subject to a resistive force given by -bv, where v is its velocity. The ratio of the damped frequency to the undamped (natural) frequency) is 0.849. If this system is subjected to a sinusoidal driving force given by

F(t)=(8.00 N)sin(0.901wo t) ,

what is the (steady-state) amplitude (in cm) of the resulting sinusoidal motion?

i know how to find the damping force 'b' and gamma, and Q, and r for the amplitue question, but why does the question give us that F(t) equation and what do we need it for I am just stumped any help would be useful

 

[member 553083]

. The equation for F(t) (the sinusoidal driving force) gives you the parameters of the external force that is being applied to the system. This is important to know because it affects the amplitude of the resulting motion. To calculate the steady-state amplitude, you need to use the equation A = F₀/((mωo)²-(b/m)²)¹/₂, where F₀ is the amplitude of the driving force and m is the mass of the object. In this case, F₀=8 N and m=0.269 kg, so you can plug in these values to get the amplitude.