Simple Harmonic Oscillator - Oscillations and Waves - Past Paper, Exams of Physics

Download Simple Harmonic Oscillator - Oscillations and Waves - Past Paper and more Exams Physics in PDF only on Docsity! KEELE UNIVERSITY DEGREE EXAMINATIONS 2009 LEVEL 1 (PRINCIPAL COURSE) Tuesday 19 May 2009, 13.00–15.00 PHYSICS/ASTROPHYSICS MODULE PHY-10012 OSCILLATIONS AND WAVES Candidates should attempt ALL of PARTS A and B, and TWO questions from PART C. PARTS A and B should be answered on the exam paper; PART C should be answered in the examination booklet which should be attached to the exam paper at the end of the exam with a treasury tag. PART A yields 16% of the marks, PART B yields 24%, PART C yields 60%. You are advised to divide your time in roughly these proportions. Figures in brackets [ ] denote the marks allocated to the various parts of each question. Tables of physical and mathematical data may be obtained from the invigilator. Student Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Please do not write in the box below A C1 Total B C2 C3 C4 /Cont’d Page 2 PART A Tick the box by the answer you judge to be correct (marks are not deducted for incorrect answers) A1 The velocity and acceleration of a simple harmonic oscillator are 180◦ out of phase 90◦ out of phase 45◦ out of phase in phase [1] A2 A block of mass m = 0.1 kg on the end of a spring with k = 0.4 N m−1 is pulled 0.2 m away from equilibrium and released from rest. Its maximum acceleration is 0.08 m s−2 0.4 m s−2 0.8 m s−2 3.2 m s−2 [1] A3 When a particle in simple harmonic motion passes through its equilibrium position, its kinetic energy equals the total energy equals half the total energy equals the potential energy equals zero [1] A4 The motion of a pendulum is approximately simple harmonic in the limit of short length small angles weak gravity low bob mass [1] A5 An oscillator of mass 100 g and natural angular frequency 3 s−1 is subject to a damping force −γẋ , with γ = 0.9 kg s−1. This system is underdamped critically damped resonantly damped overdamped [1] A6 An oscillator with mass m and natural angular frequency ω0 is damped by a force Fdamp = −γẋ . Motion will be oscillatory, with a well-defined period, if γ > 2mω0 γ = 2mω0 γ < 2mω0 γ < √ 2 mω0 [1] A7 A damped oscillator with natural angular frequency ω0 is driven by an external harmonic force with angular frequency ωe = ω0. Which one of the following is not true in the steady state? the external force cancels the oscillator’s natural restoring force the power input by the external force is a maximum the power dissipated by the damping force is a maximum the velocity of the oscillator is in phase with the external force [1] /Cont’d Page 5 B3 A simple pendulum is made by attaching a ping-pong ball with a mass of 15 grams to a length of string with negligible mass. The force of air resistance on the ball is Fair = −γẋ , with γ = 0.025 kg s−1. If the pendulum is critically damped by this force, what is the length of the string? [3] B4 A damped oscillator with natural angular frequency ω0 is driven by a force F (t) = F0 cos(ωet). Write the general expressions for the displacement and velocity as functions of time in the steady state. Sketch the velocity amplitude as a function of ωe for a lightly damped system. Identify the value of ωe that gives velocity resonance. [3] /Cont’d Page 6 B5 A harmonic wave travelling in the −x direction has a wavelength of 0.1 m, a frequency of 3400 Hz, and an amplitude of 10−6 m. Write the wave function y(x, t), given that y = 5 × 10−7 m at x = 0 at t = 0. [3] B6 Write the one-dimensional wave equation, and show that the function y(x, t) = 2 x3 + 24 x t2 is a solution. What is the wave speed, if x and y are measured in metres and t in seconds? [3] /Cont’d Page 7 B7 A violin string with linear mass density 0.003 kg m−1 is tuned by putting it under a tension of 580 N. It then vibrates at a frequency of 666 Hz in its fundamental mode. What is the length of the vibrating part of the string? [3] B8 Monochromatic light illuminates a slit of width 0.3 mm, creating a diffraction pattern on a screen 2 m away from the slit. The first-order minima on the screen are located ±3.7 mm on either side of the central intensity peak. What is the wavelength of the light? [3] /Cont’d