Spring on a tilted table with air resistance

[tarletontexan]

Homework Statement

an object of .4kg is attached to a spring with given spring constant 400 N/m. it is moving on a tilted table, that is at 30 deg from teh horizontal. The table is frictionless, but there is a dampening force -bv proportional to velocity. when the object is driven, the resonance frequency is .990 times the dampened frequency. What is the value of b

Homework Equations

f=-.5kx and the conservation of energy

The Attempt at a Solution

I know that the driven frequency is equal to something (cant remember what) and so is the dampened frequency( can't remember that either). would finding these quantities help me to find B??

 

[mark726]

Hello,

Yes, finding the driven frequency and dampened frequency would definitely help you in finding the value of B. To find the driven frequency, you can use the formula f = ω/2π, where ω is the angular frequency. The angular frequency can be found using the formula ω = √(k/m), where k is the spring constant and m is the mass of the object. Similarly, the dampened frequency can be found using the formula f = √((k/m) - (b/2m)^2).

Once you have found the driven frequency and dampened frequency, you can set them equal to each other and solve for B. This will give you the value of B that satisfies the given conditions.

Additionally, you can also use the conservation of energy to find the value of B. Since the table is frictionless, the total energy of the system (kinetic + potential) will remain constant. You can set up an equation using the energy at resonance frequency and the energy at dampened frequency and solve for B.

I hope this helps. Let me know if you have any further questions. Good luck!