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Energy of a Mass–Spring System A mass–spring oscillator consists of a 1.00 kg mass and a spring with a spring constant of 200 N/m. The oscillator is set in motion by stretching the spring 0.300 m and releasing the mass from rest. (a) What is the total energy of the mass–spring system? (b) What is the maximum speed of the mass as it oscillates? (c) What is the speed of the mass when it is 0.100 m from the equilibrium position? (d) For which displacements of the mass is the kinetic energy half its total energy?
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Polymer Physics
Period and Length of a Simple Pendulum You need to design a simple pendulum that has a period of 1.00 s. The acceleration due to gravity in your lab is 9.81 m/s2. What should the length of the string be?
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Polymer Physics
A Cardboard Sheet as a Physical Pendulum Consider a square sheet of cardboard with a mass of 20.0 g and a length of 28.0 cm. The sheet is free to rotate about a pivot point, P, that is located directly above the centre of mass of the sheet and 1.00 cm from the top edge. Calculate the period for small angular displacement about the pivot point, P.
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Polymer Physics
Determining an Equation for Simple Harmonic Motion from a Displacement Graph Figure 13-27 shows a graph of displacement x(t) versus time t for a particle. From this graph, determine an equation for x(t).
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Polymer Physics
Determining an Equation for Simple Harmonic Motion from Position and Velocity Graphs Position and velocity graphs of a simple harmonic oscillator are shown in Figure 13-28. Determine the equation of motion for the oscillator from these graphs.
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Polymer Physics
A Boat Stuck at Hopewell rocks during Low Tide At 09:00, you find that your sailboat is stuck in 0.3 m deep water during low tide at Hopewell Rocks in the Bay of Fundy (Figure 13-30). You look at the tide table and verify that the next high tide is at 15:15, when the water height will be 13.1 m. Your boat needs a water depth of at least 3.0 m to float. Assuming that the tides cause the water height at Hopewell Rocks to change in harmonic motion, estimate the earliest time when your boat will be able to float. Use the tide data given in Table 13-2.
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Polymer Physics
A Damped Harmonic Oscillator A damped harmonic oscillator consisting of a block of mass 2.00 kg and a spring of spring constant 10.0 N/m has an amplitude of 25.0 cm at t = 0 s. The amplitude falls to 75.0% of its initial value after four oscillations. Assuming that the damping force is of the form F_(D,x)=-〖bv〗_x, calculate the value of the damping constant, b the amount of energy lost during four oscillations
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Polymer Physics
Distance and Displacement You are walking briskly at a constant pace from your summer job downtown to the coffee shop. The trip takes you 400 m down one street and another 300 m along another street after turning left. What distance have you covered? What is your displacement?
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Polymer Physics
