Question
Student claims that the motion of the maiss mav be represented by the equation V-Asin(Wt) for the oscillation in the following figure: Give tWo reasons whv che use of this equation is inappropriateVacmThe oscillation is damped and the amplitude is not constant.the oscillations is forced and the oscillation is damped.There is no resistance force and the amplitude is not constant_The amplitude is constant and there is no resistance force_none of them:
student claims that the motion of the maiss mav be represented by the equation V-Asin(Wt) for the oscillation in the following figure: Give tWo reasons whv che use of this equation is inappropriate Vacm The oscillation is damped and the amplitude is not constant. the oscillations is forced and the oscillation is damped. There is no resistance force and the amplitude is not constant_ The amplitude is constant and there is no resistance force_ none of them:
Answers
Consider the spring in the figure repeated with Exercise 7, but assume that because of friction and other resistive forces, the amplitude is decreasing over time, and that $t$ seconds after the spring is released, its position in inches is given by the function $$s(t)=-11 e^{-0.2 t} \cos 0.5 \pi t$$. How many complete oscillations will the graph make during 12 sec?
For this problem. For this problem, we are describing the motion of a damped pendulum. The equation s f t equals negative 11 e to the power of negative to negative 0.2 get 0.2 t times coasts of 0.5 pi times t because of 0.5 0.5 pi t So we want to answer how Maney complete oscillations will this graph may during 12 seconds so we can figure that out. Bye. First looking at what? The frequency. So we have our own mega equal to 0.5 pi or one half pipe and our frequency is given by omega over two pi. So we have one half pie divided by two pi. She's going to give us one half divided by two or 1/4. So that tells us that we have 1/4 oscillations per second. Now, since we have 1/4 oscillations per second, that means that the number of oscillations in 12 seconds for 12 seconds is going to equal 1/4 times 12. So 1/4 times 12 is going to be 12 divided by 4 12 divided by four is three. So it's going to make three oscillations over the course of 12 seconds
Were asked to find the frequency of the oscillation of this function and we were given the frequency is equal toe one over p where P is the period in order calculate, period. You know that that is equal to two pi over the number attached to T, which is three. So the frequency is hence equal to 1/2 pi over three, which would be equal to 3/2 pi, and that would be the frequency the oscillation for this given function.
So we're told our frequency is equal to one over a period. But we don't know our periods. We need to find that Y is equal to three co sign of tea over to Well, tears are variable here. So our co efficient to that variable is 1/2. So to find a period to pie divided by 1/2 which is equal to four pi. So now to find our frequency we're gonna dio is equal to 1/4 pi and that is our frequency.
Were asked to find the frequency of this function. And it tells us that the frequency is equal to one over P where P is the period since we know that the period is equal to two pi two pi over the number that has attached to X or in this case, T that'll be two pi over 1/2 which is equal to four pi and that's the period. So frequency, which is equal to one over the period, will be equal to 1/4 pi, and that will be the frequency of the given function.