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Vibrations and Waves: Spring-Mass System and Simple Harmonic Motion

Learn about the principles of Hooke's Law, spring-mass systems, and simple harmonic motion. Discover how to calculate spring constants, periods, frequencies, and more.

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Vibrations and Waves: Spring-Mass System and Simple Harmonic Motion

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  1. Chapter 11 • Vibrations and Waves

  2. Spring-mass system

  3. Hooke’s Law • Felastic = -k x • F = elastic spring force (Newtons) • K = spring constant (Newtons/meter) • X = length stretched or compressed from equilibrium

  4. Simple Harmonic Motion • Repetitive or oscillating motion about an equilibrium as a result of a restoring force that is proportional to displacement

  5. Simple Harmonic Motion Continued • Occurs when restoring force is proportional to displacement. • The maximum displacement from equilibrium is called the amplitude. • The frequency and period depend on the setup, and are independent of the amplitude.

  6. Frequency and Period • Frequency: The number of cycles or oscillations per unit time • Measured in Hertz (Hz) • 1 Hz = 1 cycle per second • Period: The time for one cycle • f = 1/T • T = 1/f

  7. Springs in Oscillation • The period of a spring-mass system in oscillation can be described by…

  8. Example • A spring is stretched downward 5.0 cm vertically from is relaxed position when a 500 gram mass is attached. • What is the value of its spring constant? • What would its period and frequency of oscillation be if set into simple harmonic motion?

  9. Example • A 350 g mass is attached to a spring with 112 N/m spring constant. • Find the distance the spring stretches. • If the 350 g mass is taken off, how much mass should be placed on there so that it oscillates with a frequency of 1.6 Hz?

  10. Pendula

  11. Example • How long must a pendulum clock be made so that it keeps a time period of 2.00 seconds in a location where the acceleration due to gravity is 9.805 m/s2?

  12. Example • On the moon, a 1.500 m long pendulum is observed to oscillate 9.87 cycles in one minute. What is the acceleration due to gravity at that location on the moon?

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