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Ch 14: Periodic Motion
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 14: Periodic MotionProblema 24a
Capitolo 14, Problema 24a

For the oscillating object in Fig. E14.4, what is its maximum speed?
Graph depicting position vs. time for a simple harmonic oscillator, illustrating periodic motion.

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Identify the amplitude (A) of the oscillation from the graph. The amplitude is the maximum displacement from the equilibrium position, which is the highest point on the graph.
Determine the angular frequency (ω) of the oscillation. This can be found using the formula ω = 2π/T, where T is the period of the oscillation. The period is the time it takes for one complete cycle, which can be measured from the graph.
Use the formula for maximum speed in simple harmonic motion, which is v_max = Aω. This formula relates the maximum speed to the amplitude and angular frequency.
Substitute the values of amplitude (A) and angular frequency (ω) into the formula to find the maximum speed.
Ensure the units are consistent when substituting into the formula. If the amplitude is in centimeters, convert it to meters if necessary to match the standard SI units for speed (meters per second).

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Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of periodic motion where an object oscillates around an equilibrium position. The motion is characterized by a restoring force proportional to the displacement from the equilibrium, leading to sinusoidal position, velocity, and acceleration graphs. In the context of the given question, the oscillating object follows a predictable pattern, allowing for the calculation of maximum speed.
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Maximum Speed in SHM

The maximum speed of an object in Simple Harmonic Motion occurs as it passes through the equilibrium position. This speed can be calculated using the formula v_max = ωA, where ω is the angular frequency and A is the amplitude of the motion. Understanding this relationship is crucial for determining the maximum speed from the position vs. time graph provided.
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Amplitude and Angular Frequency

Amplitude is the maximum displacement from the equilibrium position in oscillatory motion, while angular frequency (ω) relates to how quickly the object oscillates, measured in radians per second. The amplitude can be identified from the graph as the maximum height reached, and the angular frequency can be derived from the period of the oscillation, which is the time taken for one complete cycle.
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Circumference, Period, and Frequency in UCM
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For the oscillating object in Fig. E14.4, what is its maximum acceleration?

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