Physics · Oscillations · NEET
No. Phase is the full angle (wt + phi) and it changes with time. The phase constant phi is just one fixed number: the value of the phase at t = 0. Phase is the moving clock hand, phase constant is where the hand pointed when you started the clock.
phi only tells you the starting position and starting direction of the particle at t = 0. It does not change the amplitude A, the frequency, or the shape of the motion. Two SHMs with the same A and same w but different phi are identical in size and speed, they just start at different points.
If x = 0 at t = 0 and the particle moves in the positive direction, then x = A sin(wt) fits, so phi = 0. If it starts at the mean position but moves in the negative direction, phi = pi (180 degrees). So starting at the centre gives phi = 0 or pi.
At an extreme, x = +A at t = 0. Put t = 0 in x = A sin(phi) = A, so sin(phi) = 1, which gives phi = pi/2 (90 degrees). This is why starting from an extreme is often written as x = A cos(wt), because cos(wt) = sin(wt + pi/2).
Phase is an angle, so its unit is the radian (rad). Sometimes it is written in degrees. wt has units (rad/s) times s = rad, and phi is also in rad, so the whole phase (wt + phi) is a pure angle.
Phase difference is how far apart in the cycle two SHMs are. If x1 = A sin(wt + phi1) and x2 = A sin(wt + phi2), the phase difference is (phi1 - phi2). If it is 0 they move together (in phase); if it is pi they move exactly opposite (out of phase).
The phase difference between displacement and acceleration of a particle in simple harmonic motion is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
wt handles how the motion advances with time. But at t = 0 the particle may not be at the mean position, so we add phi to record that starting offset. Together (wt + phi) fixes the exact stage at every moment.
Yes. phi can be any value, positive or negative, usually taken between -pi and +pi (or 0 and 2pi). A negative phi just means the motion started a little later in the cycle. Its sign only reflects the starting condition.
No. Time period depends only on w through T = 2 pi / w. The phase constant phi does not appear in the period, so it has no effect on how long one full oscillation takes.
They are the same thing. Some books write the SHM equation as x = A cos(wt + phi) or x = A sin(wt + epsilon). The symbol phi or epsilon in that bracket is the phase constant, also called the initial phase.
