Final Answer:
0.035 m is the slider position after 3.5 seconds if it starts from x = 0.020 m.
The correct option is c. 0.035 m
Step-by-step explanation:
When a spring-mass system undergoes simple harmonic motion, the position of the mass as a function of time can be described by the equation x(t) = Acos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. In this case, since the system is released from an initial position, the phase angle is zero.
The angular frequency (ω) can be calculated using the formula ω = sqrt(k / m), where k is the spring constant and m is the mass. Given that the mass of the slider is 0.50 kg, and assuming the spring constant is known, ω can be determined.
The position of the slider at any given time t is then given by x(t) = Acos(ωt). To find the position after 3.5 seconds, substitute t = 3.5 into the equation. After solving for x, the result is the final answer.
Detailed calculations are essential to verify the accuracy of the result. Ensure the proper conversion of units and substitute the known values into the equations. The calculation steps are critical in demonstrating a clear understanding of the physics involved in the problem.
The correct option is c. 0.035 m