Physics · Oscillations · NEET
Both are correct. y = A sin(wt + phi) and y = A cos(wt + phi) describe the same SHM. They only differ by the phase constant phi (cosine is sine shifted by 90 degrees, because cos(x) = sin(x + 90 degrees)). Sine is the default when the particle starts from the mean position at t = 0. Cosine is natural when the particle starts from an extreme position at t = 0. Pick the one that matches the starting point given in the problem.
Phi is the value of the phase (the angle inside the bracket) at t = 0. It fixes the starting position and starting direction of the particle. If phi = 0, then at t = 0 the particle is at the mean position (y = 0) moving in the positive direction. A non-zero phi means the particle already has a 'head start' along its cycle when the clock reads zero.
Compare your equation with the standard form y = A sin(wt + phi). The number multiplying the sine is the amplitude A. The number multiplying t is the angular frequency w. Then time period T = 2 pi / w and frequency f = 1 / T = w / (2 pi). Example: for x = 5 sin(pi t + pi/3), A = 5 and w = pi, so T = 2 pi / pi = 2 s.
The full angle (wt + phi) is called the phase at time t; it changes as time passes and controls the instantaneous position. Phi alone is the phase constant (initial phase), a fixed number set by the starting condition. So phase = phase constant + wt. The whole bracket moves; phi stays constant.
Because sine takes an angle, not a plain count of cycles. In one time period T the phase must advance by 2 pi radians (one full circle). So the rate of change of the angle is w = 2 pi / T = 2 pi f. This w (radians per second) is the angular frequency. Ordinary frequency f (cycles per second) relates to it by w = 2 pi f.
If x = 5 sin(pi t + pi/3) m represents the motion of a particle executing simple harmonic motion, then the amplitude and time period of the motion, respectively, are
A particle P revolves in a circle. The radius, period, initial position and sense of revolution are given. The y-projection of the radius vector of the rotating particle P is (particle starts at the top, radius 3 m, period 4 s)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
y = A sin(wt + phi), where A is amplitude, w is angular frequency, t is time and phi is the phase constant. It gives the position of the particle from the mean position at any time t.
y is the displacement, A is the amplitude (maximum displacement), w is the angular frequency (2 pi / T), t is the time, and phi is the phase constant that sets the starting position at t = 0.
Read w as the number multiplying t, then use T = 2 pi / w. For example, if w = pi rad/s, then T = 2 seconds.
Yes. y = A cos(wt + phi) describes the same motion; it is just a sine shifted by 90 degrees. Use cosine when the particle starts from an extreme position at t = 0.
The maximum displacement equals the amplitude A, because the sine function has a maximum value of 1, so y goes from -A to +A.
