Question

derive phase in shm ?also write it special cases​

Answer 1

Answer:

The angle φ is known as the phase shift of the function. The velocity of the mass on a spring, oscillating in SHM, can be found by taking the derivative of the position equation: v(t)=dxdt=ddt(Acos(ωt+φ))=−Aωsin(ωt+ϕ)=−vmaxsin(ωt+φ).

You can calculate it as the change in phase per unit length for a standing wave in any direction. It's typically written using "phi," ϕ.In which y0 is the y position at x = 0 and t = 0, A is the amplitude, T is the period and "phi" ϕ is the phase constant.

Simple harmonic motion can be described as an oscillatory motion in which the acceleration of the particle at any position is directly proportional to the displacement from the mean position. It is a special case of oscillatory motion.

All the Simple Harmonic Motions are oscillatory and also periodic but not all oscillatory motions are SHM. Oscillatory motion is also called the harmonic motion of all the oscillatory motions wherein the most important one is simple harmonic motion (SHM).

In this type of oscillatory motion displacement, velocity and acceleration and force vary (w.r.t time) in a way that can be described by either sine (or) the cosine functions collectively called sinusoids.