Intro to Simple Harmonic Motion (Horizontal Springs) quiz Flashcards
Intro to Simple Harmonic Motion (Horizontal Springs) quiz
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What is simple harmonic motion in the context of a mass-spring system?
Simple harmonic motion in a mass-spring system is characterized by the oscillation of a mass attached to a spring. The spring force is proportional to the displacement (F = kx), and the system oscillates between two points, with maximum displacement at the amplitude. The velocity is zero at the amplitude and maximum at the equilibrium position. The period and frequency are inversely related, and the angular frequency is related to the frequency by Omega = frequency x 2π. How are the maximum values of displacement, velocity, and acceleration determined in simple harmonic motion?
In simple harmonic motion, the maximum displacement is the amplitude (±A). The maximum velocity is ±Aω, where ω is the angular frequency. The maximum acceleration is Aω². These values are determined using sinusoidal equations that depend on time, and the angular frequency can be calculated as the square root of k/m, where k is the spring constant and m is the mass. What is the relationship between the spring force and displacement in a mass-spring system?
The spring force is proportional to the displacement, expressed as F = kx, where k is the spring constant and x is the displacement. Where is the velocity of a mass in a mass-spring system maximum and minimum?
The velocity is maximum at the equilibrium position and zero at the amplitude points. How are period and frequency related in simple harmonic motion?
Period (T) and frequency are inversely related, with frequency equal to 1/T. What is the formula for angular frequency in terms of frequency?
Angular frequency (Omega) is related to frequency by Omega = frequency x 2π. How can you calculate the angular frequency using the spring constant and mass?
Angular frequency (Omega) can be calculated as the square root of k/m, where k is the spring constant and m is the mass. What are the maximum values of displacement, velocity, and acceleration in simple harmonic motion?
The maximum displacement is the amplitude (±A), the maximum velocity is ±Aω, and the maximum acceleration is Aω². What is the significance of the sine and cosine functions in the equations of motion for a mass-spring system?
The sine and cosine functions describe the oscillatory nature of the motion, with their maximum values indicating the maximum displacement, velocity, and acceleration. How do you determine the period of oscillation using angular frequency?
The period (T) can be determined using the formula T = 2π/Omega, where Omega is the angular frequency.
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