Physics · Oscillations · NEET
Amplitude A is the maximum distance the particle moves away from the mean (rest) position, on either side. It is always a positive length. In x = A sin(wt + phi), A is the number multiplying the sine. For x = 5 sin(pi t + pi/3) metre, amplitude = 5 m. It is measured in metres, not degrees. Amplitude tells you how far the particle swings, not how fast.
Phase is the whole angle (wt + phi) inside the sine. It changes every instant because it contains t, and it tells you the exact state (position and direction) at time t. The phase constant phi is just the value of the phase at t = 0. So phase = moving angle, phase constant = starting angle. Two SHMs with the same A and w but different phi start from different points.
Angular frequency w is how fast the phase angle grows, measured in radian per second. Ordinary frequency f is how many full oscillations happen per second, measured in hertz. They are linked by w = 2 pi f = 2 pi / T. One full cycle is 2 pi radian, so w is just f multiplied by 2 pi. In x = A sin(wt + phi), the coefficient of t is w, not f.
Write the motion in the standard form x = A sin(wt + phi). Then A is the front number (amplitude), w is the number multiplying t (angular frequency), and phi is the extra constant added inside the bracket (phase constant). Time period is T = 2 pi / w. Example: x = 5 sin(pi t + pi/3) gives A = 5 m, w = pi rad/s, phi = pi/3, and T = 2 pi / pi = 2 s.
No. For ideal SHM the time period depends only on the system (like mass and spring constant, or pendulum length and g), through w = 2 pi / T. A bigger amplitude means the particle travels farther but also moves faster, so the time for one full swing stays the same. This property, period independent of amplitude, is called isochronism.
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
The displacement of a particle executing simple harmonic motion is y = A0 + A sin wt + B cos wt. The amplitude of its oscillation is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Amplitude is in metre (m). Phase and phase constant are angles, measured in radian (rad). Angular frequency is in radian per second (rad/s).
Yes. If the particle starts from the mean position moving in the positive direction with x = A sin wt, then phi = 0. The value of phi simply records where the motion is at t = 0.
Because SHM is naturally tied to a rotating angle. Using w keeps the equations simple, as in a = -w^2 x and v = w root(A^2 - x^2). You convert to f or T at the end using w = 2 pi f = 2 pi / T.
No. Amplitude is the maximum one-sided distance from the mean position. In one full period the particle covers a path length of 4A, but its displacement returns to zero.
No. x = A cos(wt + phi) and x = A sin(wt + phi') describe the same motion; they only differ by a phase of pi/2 in the phase constant. NCERT often uses the cosine form.
