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Intro to Simple Harmonic Motion (Horizontal Springs) quiz #1

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  • What is the amplitude in a simple harmonic motion mass-spring system, and how is it defined?
    The amplitude is the maximum displacement from the equilibrium position in a simple harmonic motion mass-spring system. It is the initial distance the mass is pulled or pushed from equilibrium before being released.
  • What are the key characteristics of simple harmonic motion in a horizontal mass-spring system?
    In simple harmonic motion, the restoring force is proportional to displacement (F = -kx), the system oscillates between maximum displacements (amplitudes), velocity is zero at the amplitude and maximum at equilibrium, and the motion is sinusoidal in time.
  • Which physical system best exemplifies simple harmonic motion as discussed in the course materials?
    A mass attached to a horizontal spring oscillating back and forth is the best example of simple harmonic motion.
  • What is a true statement about an object executing simple harmonic motion in a mass-spring system?
    In simple harmonic motion, the displacement, force, and acceleration are all in sync and reach their maximum values at the amplitude, while the velocity is maximum at the equilibrium position and zero at the amplitude.
  • How do the period and frequency of four mass-spring systems in simple harmonic motion relate to their masses and spring constants?
    The period (T) of each mass-spring system is given by T = 2π√(m/k), and the frequency (f) is f = 1/T. Systems with larger mass or smaller spring constant have longer periods and lower frequencies.
  • For a simple harmonic oscillator consisting of a block of mass m attached to a spring with spring constant k, what is the angular frequency of oscillation?
    The angular frequency (ω) of a simple harmonic oscillator is ω = √(k/m).
  • If the position of a simple harmonic oscillator is given by x(t) = a cos(ωt), what are the maximum values of displacement, velocity, and acceleration?
    The maximum displacement is a (the amplitude), the maximum velocity is aω, and the maximum acceleration is aω².
  • What is the relationship between the spring force and displacement in a mass-spring system undergoing simple harmonic motion?
    The spring force is given by F = kx, where k is the spring constant and x is the displacement from equilibrium. This force acts to restore the mass to the equilibrium position.
  • Why can't the standard kinematic equations be used for a mass-spring system in simple harmonic motion?
    The acceleration in a mass-spring system is always changing and is not constant, so kinematic equations that assume constant acceleration do not apply. Instead, sinusoidal equations dependent on time are used to describe position, velocity, and acceleration.
  • What must you ensure about your calculator when using the sinusoidal equations for position, velocity, and acceleration in simple harmonic motion?
    You must ensure your calculator is set to radians mode when using these equations. This is because the angular frequency and time are multiplied in radians within the sine and cosine functions.