Question

The equation of an SHM with amplitude a and angular frequency w in which all the distances are measured from one extreme:

(a) y=a cos(wx)
(b) y=a sin(wx)
(c) y=a cos(wt)
(d) y=a sin(wt)

Answer 1

The SHM equation y = a sin(wt) describes the displacement over time with amplitude 'a' and angular frequency 'w.' Amplitude represents the maximum displacement, and angular frequency entails the frequency and period of the oscillations, which are intrinsic properties determined by the mass and force constant of the system.

Step-by-step explanation:

The equation y = a sin(wt) represents a Simple Harmonic Motion (SHM) where y is the displacement from the equilibrium position, a is the amplitude, and w (omega) is the angular frequency. The angular frequency is related to the period (T) as w = 2π / T, and the frequency (f) as f = 1 / T. In SHM, the maximum displacement a system experiences from its equilibrium position is the amplitude, A, and this occurs at the extreme positions of the oscillatory motion.

When a system is undergoing SHM, its acceleration is proportional to its displacement but in the opposite direction. The equation of motion for a mass on a spring undergoing SHM could be expressed using sine or cosine functions depending on the initial conditions, such as x(t) = A cos(wt + φ) for position, with a corresponding equation for velocity. The angular frequency in SHM is determined by the mass of the system (m) and the force constant (k).