Final answer:
When a block is displaced and released, it oscillates around the new equilibrium position. The equation of motion for this block is x(t) = A * cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle.
Step-by-step explanation:
When a block is displaced and released, it will oscillate around the new equilibrium position. In this case, the block is pulled out to a position of +0.02 m, which becomes the amplitude (A) of the oscillation. The block will move back and forth between the positions of +A and -A. The period of the motion, which is the time for one oscillation, is given as 1.57 s.
The equation of motion for this block can be represented as x(t) = A * cos(ωt + φ), where A is the amplitude, ω is the angular frequency (2π/T), t is the time, and φ is the phase angle. In this case, A = 0.02 m and T = 1.57 s, so ω = 2π/1.57 and φ can be determined based on the initial conditions of the block.
Using this equation of motion, you can analyze the position, velocity, and acceleration of the block at any given time during its oscillation.