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Sample Midterm 1

# Sample Midterm 1 - Winter 2011 Physics 6B Katsushi Arisaka...

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1 Winter 2011 Physics 6B Katsushi Arisaka Sample Exam for the First Midterm Important Remarks: The First Midterm Exam is on Monday, January 24 in class. Closed book, closed note, no calculator is allowed at the exam. You are not allowed to bring any sheet of paper with equations (i.e. a cheating sheet not allowed). The real exam will be similar to this sample, but much shorter ! Two review sessions are tentatively scheduled on o Thursday, January 20 at 2-4 pm. o Thursday, January 20 at 6-8 pm. (Location to be announced later.) Some of the difficult questions in this sample exam will be reviewed. 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, 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 can not grasp the solution quickly, you are missing some important concept in physics. Read the textbook and notebook of relevant chapters carefully. Often you can not solve the problems because your background knowledge/preparation in Mathematics is weak. If this is the case, at least, review the math by reading the Appendix of the Textbook. Try to finish by the review session on Thursday, January 20.

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2 1. Let’s explore a simple mass-spring system. A mass ( m ) is connected to a spring (with spring constant k ) as shown below. There is no friction on the floor. At t = 0, the mass is slowly displaced to the left to x = -A , then released. a. Write down the Hooke’s law and Newton’s law which describe this system when the mass is located at position x . b. By combining both together, derive the second-order differential equation (in time) for the position x . c. Assume that the solution is given by cos( ). x A t ω = Derive the speed v first, then derive the acceleration a next. d. Plot the graphs of x , v and a as a function of t . Clearly mark the maximum values (on x , v and a ) as well as the period T . e. Show that the assumption cos( ) x A t ω = indeed satisfies the second-order differential equation (given at b. above), if the angular frequency ω is given by m k = ω . f. Show that this expression of ω has the correct dimension (by applying the “dimensional analysis” in Textbook Page 8-10). g. Show the relation between Period ( T ), Frequency ( f ) and angular frequency ( ω ). Briefly describe the physics meaning of each quantity.
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Sample Midterm 1 - Winter 2011 Physics 6B Katsushi Arisaka...

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