Start by checking your notes, textbooks or internet sources about spring/mass oscillators. For part i), there's a simple equation relating natural angular frequency to mass and spring constant.
Start by checking your notes, textbooks or internet sources about spring/mass oscillators. For part i), there's a simple equation relating natural angular frequency to mass and spring constant.
I think I got part A because it's just w=(k/m)0.5 units seconds-1 But I'm confused on 2. This is like a mandatory side course for my chem degree and they have not taught this at all. I'm lost. Not sure how to start to tackle it
For part ii), you need to find an equation relating decay constant to W factor, and then you can find time to decay to 0.01*initial amplitude.
Sorry I haven't covered this is class so I'm lost. I have so far Q=(W0/r) > 0.5 I tried using (0.01W0)^2=W0^2-(r/2)^2 but that just gives me r=1.999899W0 which is basically 2W0 which is critical damping and not underdamping. I'm not sure which equation to use. I think if I knew what maths I had to do I would be able to do it but I'm lost.
Decay constant = w0/2Q t = -ln(0.01)/decay constant
I've never seen this equation in my life. How is it derived? Sorry for all the Qs and thank you for the help. I think my course instructor is a bit crap. He did not explain anything properly
I think you are over-complicating. The question asks for an expression for t in terms of Q.
Oh yh sorry I just realised it said as a function of Q, so it's just t=-2ln(0.001)Q/W0 right? Is that is because all 3 parts are worth 7 marks and I don't know if that shows enough? Maybe I'm just over thinking it. I don't know this stuff lmao sorry but thank you
For ii), you wrote an expression for t as a function of Q. Now you have to sketch this as a graph. How will the graph differ depending on what percentage of A0 the amplitude decays to? For what values of Q will there be no oscillation, and hence no exponential decay?
For ii), you wrote an expression for t as a function of Q. Now you have to sketch this as a graph. How will the graph differ depending on what percentage of A0 the amplitude decays to? For what values of Q will there be no oscillation, and hence no exponential decay?
Also, is my first part right? I got 4.45x10^13 s-1 (units is correct right?)