Chapter 14 review


    Conceptual questions
      Section 14.1
      1. Medium Describe the energy of a mass oscillating at the end of a spring.
      2. Medium Can a simple harmonic oscillator be in motion but have no internal forces acting on it?
      3. Challenging Based on your understanding of the motion of a pendulum, what can you say about the acceleration of the pendulum bob during oscillation at (a) equilibrium and (b) maximum displacement?
      4. Challenging How does gravity impact the oscillation of a mass suspended vertically from a spring?
      Section 14.2
      1. Easy You are pushing a child on a swing set. The child wants to go higher on the swing. How can you make this happen?
      2. Easy Describe the relationship between the displacement and acceleration of a swinging pendulum.
      3. Medium A pendulum has been oscillating for a minute and you begin to push it at a frequency of 1.7 Hz. The natural frequency of the pendulum is 1 Hz. Will your pushes increase or decrease the energy in the pendulum?
      4. Challenging You are trying to increase the natural frequency of a mass on a spring. Should you add or remove mass to increase the natural frequency?
      5. Challenging In 1665, Christian Huygens had two pendulum clocks standing on the floor of his room. He noticed that, no matter what state he started them in, they would always eventually reach a state in which the two pendulums swung out of phase or opposite to each other. What was going on?
      6. Challenging Centuries ago soldiers crossing a bridge learned not march together in time. Instead, they all broke stride. Why break stride?
      7. Challenging Describe how the phenomenon of resonance is related to playing a guitar.
      8. Challenging Using primary sources, such as research papers or videos, draw diagrams to distinguish among three possible explanations for the collapse of the Tacoma Narrows Bridge: forced resonance, Strouhal vortices, and aeroelastic fluttering.
        Quantitative problems
          Section 14.1
          1. An oscillator has a period of 13 s. Will it complete an integer number of full cycles of oscillations after 1.3 or 130 s? Why?
          2. Easy In cycles per hour, what is the frequency of (a) the second hand of a watch, (b) the minute hand, and (c) the hour hand?
          3. Easy The frequency of an annoying tapping sound suddenly gets twice as fast. What has happened to the period of time between tapping sounds?
          4. Easy What is the frequency of a pendulum that completes 20 cycles in 45 s? What is its period?
          5. Easy A mass suspended vertically from a spring is oscillating at 1.1 Hz. Find the period of oscillation.
          6. Easy A child on a pogo stick oscillates with an amplitude of 11 cm. What is the total distance the child travels during one period?
          7. Easy An oscillator triples in frequency. What happens to its period?
          8. Easy How many times does the Moon orbit around the Earth in the time that the Earth orbits once around the Sun?
          9. Medium A surfer estimates that the waves at a particular beach have an average height of 2.3 m, measured peak to trough. She also estimates that a buoy moves up and down at a rate of two cycles in 8 s. Using her estimates, find the total distance traveled in 12 s by a seagull riding the waves.
          10. Medium The angular frequency of an oscillator is ω = 6 rad/s. Find the period.
          11. Medium The period of a simple harmonic oscillator is 2 s. Find the angular frequency.
          12. Medium A marathon runner makes 180 steps per minute. What is the frequency at which his feet hit the ground? At 20 miles he starts to walk at 90 steps per minute. What is his new pace frequency?
          13. Medium A 3 kg mass is hanging vertically from a spring suspended from the ceiling. The mass is pulled 10 cm from its equilibrium position and released. Find the speed of the mass as it passes through the equilibrium position. The spring constant is k = 400 N/m. (Assume no friction.)
          14. Medium A 1.2 m pendulum is pulled 13° away from equilibrium and let go. What is its frequency of oscillation?

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