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 cosine function in your answer.

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

Assume similar data for the motion of the blood in your aorta. estimate how many beats of the heart it will take the blood to get from your heart to your brain. (assume that the distance from your heart to your brain is 30 cm)

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.