Physics · Oscillations · NEET
No. Every SHM is oscillatory, but not every oscillation is SHM. A motion is SHM only when the displacement is a pure sine or cosine function of time, x = A sin(wt + phi). If the motion repeats but the displacement is not sinusoidal (for example a bouncing ball or x = sin^2(wt)), it is oscillatory or periodic but NOT simple harmonic.
It is called harmonic because the displacement follows a harmonic (sine/cosine) function, the same functions that describe musical sound waves. It is called simple because it is the most basic single-frequency case, with only one amplitude and one angular frequency, not a mix of many.
Both are correct SHM equations. Sine and cosine differ only by a phase of pi/2, so a cosine is just a sine shifted in time. NCERT uses x = A cos(wt + phi). You may use either form as long as A is the amplitude, w the angular frequency and phi the phase constant. Choose the one that matches the starting position given in the question.
In SHM the acceleration is a = -w^2 x. The minus sign means the acceleration always points opposite to the displacement, that is, back toward the mean position. This restoring nature is the core reason the particle keeps oscillating instead of flying away.
Only approximately. A simple pendulum performs SHM only for small angles (roughly less than about 10 degrees), where sin(theta) is nearly equal to theta. For large swings the restoring force is no longer proportional to displacement, so the motion is oscillatory but not truly simple harmonic.
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
Try the real previous-year questions from this chapter — each with the answer and a full solution.
SHM is an oscillatory motion in which the displacement of a particle from its mean position varies with time as a sine or cosine function, x = A sin(wt + phi), so that acceleration is proportional to displacement and directed toward the mean position.
The displacement equation is x = A sin(wt + phi) or x = A cos(wt + phi), where A is amplitude, w is angular frequency and phi is the phase constant. The acceleration equation is a = -w^2 x.
A mass oscillating on a spring, a simple pendulum swinging through a small angle, and the vibration of a loaded test tube floating in water are common examples of SHM used in NEET problems.
The restoring force (or acceleration) must be directly proportional to displacement and always directed toward the mean position: F = -kx, which gives a = -w^2 x.
Yes. SHM is a special kind of periodic and oscillatory motion. Every SHM is periodic, but not every periodic motion is SHM, because SHM must be sinusoidal.
