Problem 2) In the real world, oscillators don't oscillate forever: there is always some energy loss due to effects such as friction, air resistance, or transfer of some of the energy ofthe system into heat. As a result, the amplitude of oscillation eventually decays to zero. In many situations, it is a good apprOximation to say that the amplitude decreases by the same fraction in each time step. Mathematically, this can be expressed by saying that the amplitude decays exponentially as A = AgeWe. The time to is the time that it takes for the amplitude to drop by a fraction e'1 = 0.368. A smaller to means that energy is being lost more quickly. a) 0n the axes below (or similar axes that you draw}, sketch the amplitude as a function of time in the case where An = 1m and ta = 5s, labeling the values of the amplitude at 55 and 105. Note: your graph should not have any oscillations on it yet, since we are Jlust drawing the amplitude. A (F) 05 Taking into account the decreasing amplitude, the displacement as a function of time is Age-t/tocos(wt + q). As an example, the graph below shows the displacement versus time for a realistic oscillator. A(c) 10\fc) After one full oscillation, what fraction of the initial energy does the oscillator still have