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You have been assigned to tutor a friend who is struggling with interpreting the behaviour of a linear simple harmonic oscillator using the displacement-time, velocity-time and acceleration-time graphs for undamped motion (no external forces acting), and with mechanical energy of the oscillating system. And you can only tutor in writing! So all explanations must be very clear! To assist in your explanation, you are considering a spring-block system, where the block is located at +xm at t = 0 and, upon release, oscillates left and right along the x-axis. The surface is frictionless. (See diagram below.) x = 0 The displacement, velocity and acceleration plots (as a function of time) for the motion are given below: +0 Xm a (c) a) Sketch the graphs above. Use the endpoints (at t = 0 and t = T) of the displacement-time plot and any other two points on the plot to explain the motion of the oscillator. Note that you must i) indicate all four points on your sketch of the graphs; ii) include an explanation of the oscillator's displacement, velocity and acceleration at each of these four points; iii) link your explanation to where the particle is located on its journey; iv) utilize all three plots in your explanation. (14 marks) Acceleration Velocity b) Use your selected points and the plots to suggest how you would show that the mechanical energy of an undamped oscillator remains constant with time. Explain your response. (For this part of the question, it will be up to you to determine whether or not your response requires information from all three plots.) (6 marks) You have been assigned to tutor a friend who is struggling with interpreting the behaviour of a linear simple harmonic oscillator using the displacement-time, velocity-time and acceleration-time graphs for undamped motion (no external forces acting), and with mechanical energy of the oscillating system. And you can only tutor in writing! So all explanations must be very clear! To assist in your explanation, you are considering a spring-block system, where the block is located at +xm at t = 0 and, upon release, oscillates left and right along the x-axis. The surface is frictionless. (See diagram below.) x = 0 The displacement, velocity and acceleration plots (as a function of time) for the motion are given below: +0 Xm a (c) a) Sketch the graphs above. Use the endpoints (at t = 0 and t = T) of the displacement-time plot and any other two points on the plot to explain the motion of the oscillator. Note that you must i) indicate all four points on your sketch of the graphs; ii) include an explanation of the oscillator's displacement, velocity and acceleration at each of these four points; iii) link your explanation to where the particle is located on its journey; iv) utilize all three plots in your explanation. (14 marks) Acceleration Velocity b) Use your selected points and the plots to suggest how you would show that the mechanical energy of an undamped oscillator remains constant with time. Explain your response. (For this part of the question, it will be up to you to determine whether or not your response requires information from all three plots.) (6 marks)
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a The diagram represents a linear simple harmonic motion An example is spring block system in which ... View the full answer
Related Book For
Auditing and Assurance Services
ISBN: 978-0077862343
6th edition
Authors: Timothy Louwers, Robert Ramsay, David Sinason, Jerry Straws
Posted Date:
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