Question

A weight on a spring bounces a maximum of 8 inches above and below its equilibrium (zero point). The time for one complete cycle is 2 seconds. Write an equation to describe the motion of this weight, assuming the weight is at equilibrium when t = 0.

a) y(t) = 8sin(πt)
b) y(t) = 4sin(πt)
c) y(t) = 8cos(πt)
d) y(t) = 4cos(πt)

Answer 1

The equation that describes the motion of the weight on a spring is y(t) = 8sin(πt).

Step-by-step explanation:

The equation that describes the motion of the weight on a spring is y(t) = 8sin(πt).

When a weight on a spring undergoes simple harmonic motion, the equation that represents its displacement over time is given by the equation y(t) = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase constant. In this case, the amplitude of the motion is 8 inches, which corresponds to A = 8. The time for one complete cycle is 2 seconds, which corresponds to the period T = 2. The angular frequency can be calculated using the formula ω = 2π/T, which in this case is ω = 2π/2 = π. Therefore, the equation becomes y(t) = 8sin(πt).