21:10(c) the velocity of the object(d)Is the object travelling towards or away from the equilibrium position? Explain.3 of 5Question 10:In the PhET simulation, you experiment with hanging different masses on verticalsprings. Suppose you add a mass of 1kg to the end of a spring and the spring stretches20cm.(a) What is the spring constant of the spring?You now pull the mass downwards 10cm more, and release the mass. It oscillates upand down in SHM.(b) What is the angular frequency of the oscillation?(c) What is the frequency of the oscillation?(d) What is the period of the oscillation?(e) What is the general expression for the displacement as a function of time?Question 11:An object is in SHM along the x-direction. Its motion has the following properties:The maximum amplitude is 0.04mThe time between the max and min x-values is 0.3sAt t = 0.10s, x = 0.01mFind:(a) the period(b) the angular frequency(c) the phase angle(d) the general equation of motionQuestion 12:A block of mass 4kg is attached to a spring, and undergoes simple harmonic motion witha period of T=0.35s. The total energy of the system is E = 2.5J. What is the force constantof the spring? What is the amplitude of the motion?Question 13: (MCQ)An object moves with simple harmonic motion. If the amplitude is increased by 4 andthe period is doubled, the object's maximum speed is(a) quartered.(b) halved.(c) quadrupled.(d) doubled.(e) Unchanged.2(a) c>b> a=d(b) c>b>a>d(c) d>a>b> c(d) a=d>b> c(e) b>c> a=dQuestion 14: (MCQ)Four springs have been compressed from their equilibrium position at x = 0 cm. Whenreleased, they will start to oscillate. Rank in order, from highest to lowest, the maximumspeeds of the oscillators.(a)(b)(c)(d)3kminiAkiww4m!"2m4mikamva.uwc.ac.za67 21:11PHYSICS 121Homework problems on SHMPlease do these problems on a sheet of paper and hand it in on Thursday MorningQuestion 1An object oscillates with angular frequency = 8.0 rad/s. At t = 0, the object is at x = 6 cm with an initialvelocity of -30 cm/s.(a) Find the amplitude and phase constant of the motion.(b) Write down x as function of time(c) Sketch the graphs of x(t), v(t) and a(t) vs timeQuestion 2Week 3A mass-spring system with a mass of 0.2 kg is undergoing SHM with an amplitude of 10 cm and afrequency of 2 Hz. At the equilibrium position, the potential energy is zero.(a) Write down x as function of time if motion starts (t=0s) at +A.<2023(a) the mass of the object(b) the frequency of the motion, and(c) the period of the motion(b) Calculate the total mechanical energy of the system as well as the maximum values of kinetic andpotential energies during its motion.Question 3An object oscillates with an amplitude of 5.8 cm on a horizontal spring of force constant 1.8 kN/m. It'smaximum velocity is 2.20 m/s. FindQuestion 5The period of the pendulum is given by T = 2 √acceleration due to gravity. State clearly all assumptions you make.66Question 4A 2.5 kg object hanging from a horizontal spring of force constant 600 N/m with amplitude of 3 cm. Whenthe object is at its maximum downward displacement, find(a) The total energy of the system(b) The gravitational potential energy(c) The potential energy of the spring(d) What is the maximum kinetic energy of the object (Hint: choose potential energy = 0 when the objectis in equilibrium)where L is the length of the pendulum and g isikamva.uwc.ac.za

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Question 10: In the PhET simulation, you experiment with hanging different masses on vertical springs. Suppose you add a mass of 1kg to the end of a spring and the spring stretches 20cm. (a) What is the spring constant of the spring? You now pull the mass downwards 10cm more, and release the mass. It oscillates up and down in SHM. (b) What is the angular frequency of the oscillation? (c) What is the frequency of the oscillation? (d) What is the period of the oscillation? (e) What is the general expression for the displacement as a function of time?

Question 10: In the PhET simulation, you experiment with hanging different masses on vertical springs. Suppose you add a mass of 1kg to the end of a spring and the spring stretches 20cm. (a) What is the spring constant of the spring? You now pull the mass downwards 10cm more, and release the mass. It oscillates up and down in SHM. (b) What is the angular frequency of the oscillation? (c) What is the frequency of the oscillation? (d) What is the period of the oscillation? (e) What is the general expression for the displacement as a function of time?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.52P: A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where...

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A uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35
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In an engine, a piston oscillates with simpler harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = O. find (a) the position of the particle, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
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A mass-spring system moves with simple harmonic motion along the x axis between turning points at x1 = 20 cm and x2 = 60 cm. For parts (i) through (iii), choose from the same five possibilities, (i) At which position does the particle have the greatest magnitude of momentum? (a) 20 cm (b) 30cm (c) 40 cm (d) some other position (e) The greatest value occurs at multiple points, (ii) At which position does the particle have greatest kinetic energy? (iii) At which position does the particle-spring system have the greatest total energy?
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