How is the displacement in a simple harmonic motion determined?

The displacement in a simple harmonic motion is determined by the amplitude of the oscillation.

Simple harmonic motion is a type of periodic motion where the displacement of an object from its equilibrium position is proportional to the force acting on it. The motion is described by the equation x = A sin(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.

The amplitude A represents the maximum displacement of the object from its equilibrium position. It is determined by the initial conditions of the system and is a constant value. The angular frequency ω is determined by the mass and spring constant of the system and is also a constant value. The phase angle φ represents the initial position of the object at time t=0 and can vary between 0 and 2π.

To determine the displacement of the object at any given time t, we simply plug in the values of A, ω, and φ into the equation x = A sin(ωt + φ) and solve for x. For example, if A = 2 cm, ω = 2π rad/s, and φ = π/4, then the displacement at time t = 1 s would be x = 2 sin(2π(1) + π/4) = 2√2 cm.

In summary, the displacement in a simple harmonic motion is determined by the amplitude of the oscillation, which represents the maximum displacement of the object from its equilibrium position. The displacement at any given time can be calculated using the equation x = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle.