Final answer:
The motion of a mass on a vertically hung spring, characterized by simple harmonic motion, can be described using the equation y(t) = A * cos(ωt + φ), where y(t) represents the position of the mass at time t, A is the amplitude, ω is the angular frequency, and φ is the phase constant.
Step-by-step explanation:
The motion of a mass on a vertically hung spring can be described using the equation of simple harmonic motion. Simple harmonic motion refers to the back-and-forth motion of a system in which the restoring force is directly proportional to the displacement from equilibrium. For a mass oscillating on a vertical spring, the equation of motion is given by:
y(t) = A * cos(ωt + φ)
- y(t) represents the position of the mass at time t.
- A is the amplitude of the oscillation, representing the maximum displacement from equilibrium.
- ω is the angular frequency, given by ω = 2πf, where f is the frequency of the oscillation.
- φ is the phase constant, representing any initial phase shift.
In this equation, the cosine function represents the oscillatory nature of the motion.