Now solve the differential equation V(t)=−CRdV(t)dt for the initial conditions given in the problem introduction to find the voltage as a function of time for any time t. Express your answer in terms of q0, C, R, and t.

V(t) =(q0/C) * e^(−t/RC )

Explanation:

If there were a battery in the circuit with EMF  E , the equation for  V(t)  would be  V(t)=E−(RC)(dV(t)/dt) . This differential equation is no longer homogeneous in  V(t)  (homogeneous means that if you multiply any solution by a constant it is still a solution). However, it can be solved simply by the substitution  Vb(t)=V(t)−E . The effect of this substitution is to eliminate the  E  term and yield an equation for  Vb(t)  that is identical to the equation you solved for  V(t) . If a battery is added, the initial condition is usually that the capacitor has zero charge at time  t=0 . The solution under these conditions will look like  V(t)=E(1−e−t/(RC)) . This solution implies that the voltage across the capacitor is zero at time  t=0  (since the capacitor was uncharged then) and rises asymptotically to  E  (with the result that current essentially stops flowing through the circuit).

1. The sound of the shakuhachi is deeper and deeper compared to the sound of the western flute.

2. It has the ability to be divided into three octaves on a five note scale.

3. The Japanese aesthetic quality that can be heard in the piece is the "ma", the "okua-den" lineage and the silence that can be noticed between the beats and the breath.

Explanation:

The shakuhachi is a wind instrument very popular in the east and very similar to the European recorder. It is made of bamboo and has a very simple appearance, with only a mouthpiece and 5 holes, but it has a great versatility which allows it to be used in many different genres. This versatility occurs thanks to its deep and raw sound that can be divided into three octaves and five-note scale.