A block on a spring is subjected to a daming force that is directly velocity and to applied sinusoudle force. The energy dissipated by daming is supplied by
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Answer:
wave is described by y(x,t) = 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds. The frequency is:
A) Hz
B) Hz
C) Hz
D) Hz
E) Hz
In this problem, is the amplitude, k=3\ (the angular wave number) and rad/s (the angular frequency). Then
The correct answer is D
2. Below are sets of values for the spring constant, damping constant, and mass for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?
A)
B)
C)
D)
E)
The damping time is set by and, as shown in the formula page, by .Large values of mean rapid damping. Therefore, we are looking for the SMALLEST value of among the various choices. In A), , in B) , in C) , in D) , and in E) . Clearly in case B) has the largest value and in case A) has the smallest value! The larger the value of , the more rapidly the energy dissipates. Conversely, the smaller the value of , the more slowly the energy dissipates. Therefore, the correct answer is A.
3. Two events occur 100 m apart with an intervening time interval of 0.60 s. The speed of a reference frame in which they occur at the same coordinate is:
A) 0
B) 0.25c
C) 0.56c
D) 1.1c
E) 1.8c
Here we apply the Lorentz transformation for \ such that
For we have or . Then it is easy to see that The correct answer is C.
4. A wave traveling to the right on a stretched string is shown below. The direction of the instantaneous velocity of the point P on the string is:
A)
B)
C)
D)
E) no direction since v = 0
This is quite hard. The wave moves to the right. The easiest thing to do is draw the wave at a later time, in which case we see that the point P has moved DOWN. Therefore, the point P is going to have a smaller value at later times than it has at the time shown. This means that the point P is moving DOWN. The correct answer is B.
5. A rocket ship of rest length 100 m is moving at speed 0.8c past a timing device which records the time interval between the passage of the front and back ends of the ship. This time interval is:
A) 0.20 s
B) 0.25 s
C) 0.33 s
D) 0.52 s
E) 0.69 s
There are several ways to do this problem. The easiest, perhaps, is to realize that, in our frame, the length of the rocket ship is . So we have to find when But this is not hard, and we get (plugging in the numbers) that Thus the 100 meter rocket ship looks, to us, as if it is L=60 meters long. But 60 meters at speed gives us a time of seconds. The correct answer is B.
6. Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are , , and , where x is in meters and t is in seconds. Match each mathematical form to the appropriate graph below.
A)
B)
C)
D)
E)
In these diagrams, for which you needed a magnifying glass to see carefully, we are looking at a snapshot in time. Time is frozen so we are looking at the wavelengths. We can see the wavelengths from the three equations. In i, k=3 so meters. Similarly, for the next two diagrams, and meters respectively. The shortest wavelength is \ and the longest wavelength is . This means \ is in the middle. When we look at the diagrams, we see the longest wavelength is i and the shortest is iii. So we identify \ with i and with iii. The correct answer is B.
7. In the diagram below, the interval PQ represents:
A) wavelength/2
B) wavelength
C) 2 x amplitude
D) period/2
E) period