Recent content by JNBirDy

Homework Statement Consider a RLC circuit. a) Suppose the parameters are chosen to give critical damping. The capacitor is charged to a voltage of V₀ and at time equal to zero the switch is closed. Find the time at which the magnitude of the current reaches a max, and find the value of the...

Hi, this problem is from 'Electromagnetism' by Grant & Phillips and it states, Homework Statement 'http://i1129.photobucket.com/albums/m505/physicsbird1/126fig.png" shows a cross-section of the cylindrical high-voltage terminal of a van der Graaff generator, surrounded by an 'intershield'...

Homework Statement You borrow money from a friend at a continuous interest rate of r% per month. You want to pay your friend back as quickly as you can at the beginning, but reduce your payment rate over time. You decide to pay off at a continuously decreasing rate given by K₀e^{-at}, in...

Homework Statement Suppose there is a "slab" of plasma in a gas, and let N be the density of free electrons/unit volume. If an external electric field is applied, all the electrons move upwards a distance of x, which produces a thin sheet of unbalanced negative charge -Nex per unit area at the...

Are you referring to: cos(α+β) = cos(α)cos(β) - sin(α)sin(β) cos(α-β) = cos(α)cos(β) + sin(α)sin(β) If so I don't understand how to use them in this case since 0.02 / cos(⌀) = -0.012 / cos(1.98 + ⌀) cos(1.98 + ⌀) / cos(⌀) = -0.6 ---- Maybe this is what you wanted me to do: cos(1.98 + ⌀)...

Once I have the two equations: 0.02 = Acos(⌀) -0.012 = Acos(1.98 + ⌀) How exactly do I manipulate them so that I can solve for one of them? I know that I can get them into the form, A = 0.02 / cos(⌀) A = -0.012 / cos(1.98 + ⌀) and ⌀ = arccos(0.02 / A) ⌀ = arccos(-0.012 / A) - 1.98 but...

Homework Statement Find an implicit, general solution to: dy/dx = (6x - 4y) / (x - y) with x > 0. Homework Equations The Attempt at a Solution dy/dx = (6x - 4y) / (x - y) x(dv/dx) + v = (6 - 4v) / (1 - v) [(1-v) / (v-3)(v-2)] dv = dx / x \int dv/(v-2) - 2\int...

Been working on it and I think I've figured it out. dm/dt = k*S (where k is the constant or proportionality and S is the surface area) -> S(t) = 2Pi*(h(t)r + r^2) -> p = m(t)/V(t) -> V(t) = h(t)*2Pi*r^2 -> p = m(t)/h(t)*2Pi*r^2 dm(t)/dt = k[2Pi(r*m(t)/p*2Pi*r^2 + r^2] dm(t)/dt =...

Hmm.. still not sure if I'm fully understanding it. --- The mass of the disk increases at a rate proportional to the volume as it increases in time. If I let r represent the growth rate, and dV/dt represent the change in volume w.r.t., then I get: dm/dt = r(dV/dt) This doesn't seem right to me?

Homework Statement Assuming that the rate of the mass (m) of an object is proportional to its total surface area, derive a D.E for the rate of change in the mass. Arbitrary constants may be included. The objects in question are expanding peat discs. The discs absorb water through their...

Ah, yes, I think I get it now. For some reason I was thinking that I needed to get actual numbers. Thanks.

Homework Statement i) Find all vectors v such that <1,2,1> X v = <3,1,-5> ii) Explain why there is no vector v such that <1,2,1> X v = <3,1,5> Homework Equations a X b = <a_{2}b_{3} - a_{3}b_{2}, a_{3}b_{1} - a_{1}b_{3}, a_{1}b_{2} - a_{2}b_{1}) The Attempt at a Solution i) <1,2,1> X v =...

Yes, thank you, I figured it out this morning. Silly mistake...

Homework Statement A rotating objects motion can be described by its angle (θ). Given that an objects potential energy is U = 100(1-cosθ) and its kinetic energy is K = 10(dθ/dt)^2, form a second-order differential equation. Note that Total Energy = P + K, and that total energy does not change...

What is the best way to go about solving a SHM problem that asks for amplitude and phase constant when only one initial condition (x(0)) is given? I'm a little confused because I read that to find A and the phase constant you must use the initial conditions - but I've encounter a few problems...