Sample Final

Sample Final - Winter 2011 Physics 6B Katsushi Arisaka...

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1 Winter 2011 Physics 6B Katsushi Arisaka Sample Exam for the Final Exam Important Remarks: The Final Exam is o Tue, March 15, 11:30 am-2:30 pm The exam is three-hour long, so it will contain six big questions. (The second MT had two big questions. So the final is tree times longer than the second MT!) Among six questions, one is likely to be from the range of the 1 st MT, two or three are from the 2 nd MT, and the rest will be from the lectures after the 2 nd MT (i.e. magnetism). Closed book, closed note, no calculator is allowed at the exam. In addition to this sample exam, please also review the real mid terms problems as well as the sample exam problems for both the fist MT and the second MT. It is extremely important to review your first MT and second MT, and understand why you made mistakes. Review Sessions: Two sets of review sessions are tentatively scheduled as follows. (Locations will be announced later.) The first round is for Circuits, Ampere’s Law (Problem #6- 11). o 3/1 (Tue) 11:00 – 12:50 pm (small room) o 3/3 (Thu) 2:00 – 3:50 pm o 3/3 (Thu) 6:00 – 7:50 pm The second round is for Magnetism as a whole (Problem #12- 16). o 3/8 (Tue) 11:00 – 12:50 pm (small room) o 3/9 (Wed) 6:00 – 7:50 pm o 3/10 (Thu) 2:00 – 3:50 pm How to prepare for exams: Try to solve this sample exam without opening the textbook or notebook first. (It is however not wise to spend too much time for the first time.) If you cannot solve quickly, read the lecture note or the textbook where the solution is given. Once you recognize the solution, close the textbook and notebook, and then write the answer on a white piece of paper. Do not simply copy the solution from the textbook/notebook. You’d better spend enough time until you full understand the concept. If you cannot grasp the solution quickly, you are missing some important concept in physics. Read the textbook and notebook of relevant chapters carefully.
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2 1 Let’s consider the complex system where the mass is supported by two springs, one on the right side (with Spring Constant = k ) and the other on the left side (with Spring Constant = 3k ). The second spring on the left side is not physically glued to the mass. As a result, when the mass goes to the right side, it is pushed back only by the right-side spring, k . At t = 0, the mass is suddenly hit by a hammer (from the left to the right) and acquires the initial velocity v = v 0 (to the right direction) . First, let’s consider only when x > 0, where the mass has angular frequency ω , period T, amplitude A. a) By combining Newton’s law and Hooke’s law, derive the second-order differential equation (in time) for the position x (for x > 0). b) Show that the assumption sin( ) xA t ωφ =+ satisfies the second-order differential equation (given in a) above), if the angular frequency satisfies m k = .
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Sample Final - Winter 2011 Physics 6B Katsushi Arisaka...

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