Final answer:
The first time when the mass is at the position x = 0 is at t = 0.095s, as obtained by solving the equation x = (12.4 cm) cos[2πt/(0.38s)] for t when x is zero.
Step-by-step explanation:
To find the first time that the mass is at the position x = 0 given the equation x = (12.4 cm) cos[2πt/(0.38s)], one needs to solve the equation for t when x is zero. Since the cosine function equals zero at π/2 and its odd multiples, we set the argument of the cosine equal to π/2 to find the first instance.
cos[2πt/(0.38s)] = 0 → 2πt/(0.38s) = π/2 → t = (0.38s/4)
Solving for t, we get:
t = (0.38s/4) = 0.095s
So, the mass is first at the position x = 0 at t = 0.095s.