Question

When a piece (mass 25 g) is placed on the spring, the spring stretches 0.040 m. The piece is pushed from its equilibrium position by giving it an initial velocity of 0.70 m/s straight down. Specify movement amplitude and cycle time.

Options:
a. Amplitude: 0.040 m, Cycle Time: 1.5 s
b. Amplitude: 0.020 m, Cycle Time: 0.75 s
c. Amplitude: 0.040 m, Cycle Time: 0.75 s
d. Amplitude: 0.020 m, Cycle Time: 1.5 s

Answer 1

The movement amplitude is 0.040 m and the cycle time is 1.5 s.

Step-by-step explanation:

To find the movement amplitude and cycle time, we can use the formula for the period of oscillation of a mass-spring system. Given that the mass of the object is 25 g and the spring stretches 0.040 m, the movement amplitude is equal to the stretch of the spring, which is 0.040 m. The cycle time can be found using the formula: T = 2π√(m/k), where m is the mass and k is the spring constant. Substituting the given values, we get: T = 2π√(0.025 kg / 10 N/m) = 1.5 s. Therefore, the correct answer is option (a): Amplitude: 0.040 m, Cycle Time: 1.5 s.