Yes, in a simple harmonic motion (SHM), the displacement will oscillate between positive and negative values, but it will always eventually return to zero. This is because SHM follows a periodic pattern, meaning it repeats itself over and over again.
The time it takes for a SHM to reach zero displacement depends on the amplitude, frequency, and initial conditions of the motion. In general, the period of a SHM (the time it takes to complete one full cycle) is given by T = 2π√(m/k), where m is the mass and k is the spring constant. So the time it takes to reach zero displacement will be half of the period.
Yes, a SHM can reach zero displacement multiple times. As mentioned before, a SHM follows a periodic pattern, so it will oscillate between positive and negative values, crossing zero displacement multiple times in one cycle.
The main factors that affect whether a SHM will reach zero displacement are the amplitude, frequency, and initial conditions of the motion. The amplitude is the maximum displacement from the equilibrium position, the frequency is the number of oscillations per unit time, and the initial conditions refer to the starting position and velocity of the object.
No, it is not possible for a SHM to never reach zero displacement. As mentioned before, SHM follows a periodic pattern and will always return to its equilibrium position. Even if the amplitude is very small or the frequency is very high, the object will still eventually reach zero displacement.