Final answer:
The period of the simple harmonic motion equation d=5sin((pi/4)t) is d) 2π. The period, T, can be found by the formula 2π/ω, with ω being the angular frequency. For a spring-mass system, the period is determined by T = 2π√(m/k).
Step-by-step explanation:
The simple harmonic motion equation d=5sin((pi/4)t) describes the displacement of a particle in simple harmonic motion as a function of time. The variable t represents time and the term (pi/4)t indicates the angular frequency, ω, of the motion.
The period of simple harmonic motion is the time taken for one complete cycle of motion, and it is equal to 2π/ω. Since the angular frequency ω is pi/4, the period T is therefore 2π/(pi/4), which simplifies to 8. So the correct answer to the question is d) 2π.
Similarly, considering examples provided for simple harmonic motion, we can relate another example where a particle of mass 100 g attached to a spring with spring constant 40 N/m undergoes simple harmonic motion. The period of oscillation can be determined by using the formula T = 2π√(m/k), where m is the mass and k is the spring constant.
The period of oscillation influences the behavior of systems undergoing simple harmonic motion, like pendulums and springs, and is a fundamental characteristic of oscillatory systems.