PHY131H1S - Class 21
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Transcript of PHY131H1S - Class 21
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PHY131H1S - Class 21Today:• Oscillations,
Repeating Motion• Simple Harmonic
Motion• Oscillations / Circular
Motion Connection• Potential and Kinetic
Energy in Oscillations
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A little pre-class reading quiz on Ch.14…
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Last day I asked at the end of class:
• A block is oscillating on a spring with a period of 2 seconds.
• What is the period if the mass is doubled?• ANSWER:
• What is the period if the spring constant is doubled?
• ANSWER:
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Some oscillations are not sinusoidal:
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Period, frequency, angular frequency
• The oscillation frequency f is measured in cycles per second, or Hertz.
• We may also define an angular frequency ω in radians per second, to describe the oscillation.
• The time to complete one full cycle, or one oscillation, is called the period, T.
• The frequency, f, is the number of cycles per second. Frequency and period are related by
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The Spring-Mass System
The force exerted on the mass by the spring: F = −k x (Hooke’s Law) F = m a (Newton’s Second Law)
Combine to form a differential equation:
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Weird coincidence noted by Knight:
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This is the position graph of a mass on a spring. What can you say about the velocity and the force at the instant indicated by the dotted line?
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This is the position graph of a mass on a spring. What can you say about the velocity and the force at the instant indicated by the dotted line?
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Simple Harmonic MotionIf the initial position of an object in SHM is not A, then we may still use the cosine function, with a phase constant measured in radians.In this case, the two primary kinematic equations of SHM are:
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• An object moves with simple harmonic motion. If the amplitude and the period are both increased by a factor of 2, the object’s maximum speed is
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equilibrium
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Gravitational Potential Energy increases with height. Elastic Potential Energy increases as a spring is stretched. Kinetic Energy increases with speed.
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Before Class 22 on Wednesday• Please finish reading Knight Chapter 14
• Something to think about: A mass hanging from a string is swinging back and forth with a period of 2 seconds.
• What is the period if the mass is doubled?• What is the period if the length of the string is
doubled?