To determine the distance traveled by a particle undergoing Simple Harmonic Motion (SHM), we need to consider the formula for displacement in SHM as a function of time:
x(t) = A * cos(2πt / T)
Where: x(t) is the displacement of the particle at time t, A is the amplitude of the motion, t is the time, and T is the period of the motion.
Given that the amplitude (A) is 10 cm and the period (T) is 4 seconds, we can substitute these values into the equation:
x(t) = 10 * cos(2πt / 4)
To find the distance traveled in 8 seconds, we need to evaluate the displacement at t = 8:
x(8) = 10 * cos(2π * 8 / 4) = 10 * cos(4π) = 10 * cos(0) = 10 * 1 = 10 cm
Therefore, the particle would travel a distance of 10 cm in 8 seconds.