MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm Print Print View physics 2211 MP14 Chapter 14 View Grading Details Due at 5 30pm on Sunday November 25 2007 Position Velocity and Acceleration of an Oscillator Learning Goal To learn to find kinematic variables from a graph of position vs time The graph of the position of an oscillating object as a function of time is shown Some of the questions ask you to determine ranges on the graph over which a statement is true When answering these questions choose the most complete answer For example if the answer B to D were correct then B to C would technically also be correct but you will only recieve credit for choosing the most complete answer Part A Where on the graph is ANSWER Part B Where on the graph is A to B A to C C to D C to E B to D A to B and D to E 1 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm ANSWER A to B A to C C to D C to E B to D A to B and D to E Part C Where on the graph is ANSWER A only C only E only A and C A and C and E B and D ANSWER A to B A to C C to D C to E B to D A to B and D to E Part E Where on the graph is the velocity ANSWER A to B A to C C to D C to E Part D Where on the graph is the velocity Hint D 1 Finding instantaneous velocity Hint not displayed 2 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm Hint not displayed Hint not displayed B to D A to B and D to E Part F Where on the graph is the velocity Hint F 1 How to tell if ANSWER A only B only C only D only E only A and C A and C and E B and D Part G Where on the graph is the acceleration Hint G 1 Finding acceleration ANSWER A to B A to C C to D C to E B to D A to B and D to E Part H Where on the graph is the acceleration ANSWER A to B A to C 3 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm C to D C to E B to D A to B and D to E Part I Where on the graph is the acceleration Hint I 1 How to tell if ANSWER A only B only C only D only E only A and C A and C and E B and D Hint not displayed Harmonic Oscillator Acceleration Learning Goal To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time One end of a spring with spring constant The block rests on a frictionless horizontal surface The equilibrium position of the left side of the block is defined to be is attached to the wall The other end is attached to a block of mass The length of the relaxed spring is The block is slowly pulled from its equilibrium position to some position the block is released with zero initial velocity along the x axis At time The goal of this problem is to determine the acceleration of the block and as a function of time in terms of It is known that a general solution for the position of a harmonic oscillator is 4 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm where and are constants Your task therefore is to determine the values of and then use the and connection between to find the acceleration in terms of and and Part A Combine Newton s 2nd law and Hooke s law for a spring to find the acceleration of the block time as a function of Hint A 1 Physical laws Combine the expressions for Hooke s law coordinate is zero the deformation of the spring at any time equals the coordinate of the block and Newton s 2nd law Note that since the initial Express your answer in terms of and the coordinate of the block ANSWER The negative sign in the answer is important It indicates that the restoring force the tension of the spring is always directed opposite to the block s displacement When the block is pulled to the right from the equilibrium position the restoring force is pulling back that is to the left and vice versa Part B Using the fact that acceleration is the second derivative of position find the acceleration of the block function of time Express your answer in terms of and as a ANSWER Part C 5 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm Find the angular frequency Hint C 1 Using the previous results In the previous parts you obtained two expressions for Compare these expressions to determine Express your answer in terms of and ANSWER Note that the angular frequency physical characteristics of the system or the amplitude of the motion and therefore the period of oscillations depend only on the intrinsic and Frequency and period do not depend on the initial conditions Vertical Mass and Spring Oscillator A block of mass when the spring is stretched a distance is attached to the end of an ideal spring Due to the weight of the block the block remains at rest from its equilibrium length The spring has an unknown spring constant and Part A 6 of 14 11 18 07 7 34 PM MasteringPhysics Assignment Print View http session masteringphysics com myct assignmentPrint assignm Part B Suppose that the block gets bumped and undergoes a small vertical displacement Find the resulting angular frequency of the block s oscillation about its equilibrium position Hint B 1 Formula for angular frequency The angular frequency of simple harmonic motion for a body of mass constant is given by acted on by a restoring force with force Express the frequency in terms of given quantities and due to gravity the magnitude of the acceleration ANSWER It may seem that this result for the frequency does not depend on either the mass of the block or the spring constant which might make little sense However these parameters are what would determine the extension of the spring when the block is hanging One way of thinking about this problem is to consider both both fairly simple measurements and knowing the mass you can determine the value of the spring constant and the acceleration due to gravity experimentally as unknowns By measuring and and Damped Egg on a Spring A 50 0 hard boiled egg moves on the end of a spring with …