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Periodic motion is a repeating oscillation. The time for one oscillation is the period T and the number of oscillations per unit time is the frequency f. These quantities are related by \(f = \frac{1}{T}\).
We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let’s try one example of each. A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs.
1. One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23.1.1) where A > 0 is the amplitude (maximum value).
We can use the formulas presented in this module to determine the frequency, based on what we know about oscillations. Consider a medical imaging device that produces ultrasound by oscillating with a period of 0.400 \(\mu\)s.
The period formula, T = 2π√m/k, gives the exact relation between the oscillation time T and the system parameter ratio m/k. When you think about it, the dependence of T on m/k makes perfect intuitive sense.
Finding the period of oscillation for a pendulum We can calculate the period of oscillation Period is independent of the mass, and depends on the effective length of the pendulum. g L T L g f S S, 2 2 1
We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let’s try one example of each. (a) A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs.
