Final answer:
The maximum speed of a 53 g oscillating mass described by the equation x(t) = (1.6 cm) cos(10t) is found by multiplying the amplitude (0.016 meters) with the angular frequency (10 rad/s), resulting in a maximum speed of 0.16 m/s.
Step-by-step explanation:
The student's question deals with the maximum velocity of a 53 g oscillating mass given by the position-time relation x(t) = (1.6 cm) cos(10t), where t is in seconds. According to physics, when dealing with simple harmonic motion, the maximum speed (Vmax) occurs when the oscillating object passes through the equilibrium position. The formula to determine maximum speed is Vmax = Aω, where A is the amplitude of oscillation, and ω is the angular frequency.
Given the equation x(t) = (1.6 cm) cos(10t), we can see that the amplitude A is 1.6 cm (or 0.016 meters), and the angular frequency ω is 10 rad/s. Therefore, to give a complete calculated answer, we simply multiply these two values:
Vmax = Aω = 0.016 m × 10 rad/s = 0.16 m/s
The maximum speed of the oscillating mass is 0.16 meters per second.