Question regarding Damped, Driven Harmonic Oscillatis

[Stellar1]

Homework Statement

A mass m moves along the x-axis subject to an attractive force given by 17B^2mx/2 and a retarding force given by 3Bmx', where x is the distance from the origine and B is a costant. A driving force given by mAcos(wt), where A is a constant, is applied to the particle along the x-axis. Find the driving frequencies at which the mechanical energy of the forced oscillation is one half of its maximum value.

Homework Equations

E=1/2kA(w)^2


I just wanted to run this by you guys. It makes sense to me and I wanted to get external input. I calculated the amplitude of the oscillation with reference to omega and plugged that into the equation (lets call it 1/2kA(w')). What I did next was I derived the energy equation and found a value for w. I then equated 1/2kA(w)^2 with 1/4kA(w')) and solved for w. I ended up having to use the quadratic equation to find it. Does this sound right to you?

 

[Jhero]

Your approach seems to be on the right track. However, I would suggest double checking your calculations and equations to ensure that they are accurate. It may also be helpful to provide some more context and background information on the problem, such as the specific values of m, B, and A, as well as any other relevant information. This will help to ensure that your solution is complete and accurate.

Additionally, it may be helpful to provide a brief explanation of your thought process and reasoning behind your approach, as this will help others to understand and potentially provide feedback or alternative solutions.

Overall, it seems like you have a good understanding of the problem and are on the right track towards finding a solution. Keep up the good work and don't be afraid to ask for further clarification or assistance if needed. Good luck!