From mechanics, you may recall that when the acceleration of an object is proportional to its coordinate, d2xdt2=−kmx=−ω2x, such motion is called simple harmonic motion, and the coordinate depends on time as x(t)=acos(ωt+ϕ), where ϕ, the argument of the harmonic function at t=0, is called the phase constant. find a similar expression for the charge q(t) on the capacitor in this circuit. do not forget to determine the correct value of ϕ based on the initial conditions described in the problem. express your answer in terms of q0, l, and c. use the cosi

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

The mantle is made up of which structural zones?

What are the dimensions of the cross section that passes through the points a, f, g, and d?