Physics · Oscillations · NEET
The minus sign shows direction. When the particle moves to the right of the mean position (x is positive), the force acts to the left (F is negative), pulling it back. When it moves to the left (x is negative), the force acts to the right (F is positive). So the force always points toward the mean position, opposite to the displacement. This is why it is called a restoring force. Without the minus sign the force would push the particle away and there would be no oscillation.
Not always. In F = -kx, k is called the force constant and it equals m*w^2 (mass times angular frequency squared). For a real spring-block system this force constant happens to be the same as the spring constant k of the spring. But for other SHM systems, like a pendulum, k just means m*w^2 and has nothing to do with a physical spring. So k is a general SHM force constant, and the spring constant is only one special case of it.
They say the same thing in two forms. Start from acceleration: a = -w^2 x. Multiply both sides by mass m: m*a = -m*w^2*x. By Newton's second law m*a = F, so F = -(m*w^2)*x = -kx, where k = m*w^2. So a = -w^2 x is the acceleration form and F = -kx is the force form of the exact same SHM condition.
Yes. Any motion in which the net restoring force is directly proportional to the displacement and opposite in direction (F = -kx) is simple harmonic motion. NCERT states this clearly: only that periodic motion governed by the force law F = -kx is simple harmonic. If the force depends on x in any other way, for example F proportional to -x^3 or -x^2, the motion is oscillatory but NOT simple harmonic.
Since k = m*w^2, rearrange to get w = square root of (k/m). Then time period T = 2*pi / w = 2*pi * square root of (m/k), and frequency f = 1/T = (1/2pi) * square root of (k/m). So once you know the force constant k and mass m from the force law, you can directly get w, T and f.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The force law for SHM is F = -kx, where F is the restoring force, x is displacement from the mean position, and k = m*w^2 is the force constant. The force is proportional to displacement and directed opposite to it, toward the mean position.
In F = -kx, the force constant k equals m*w^2, that is mass times the square of the angular frequency. From this, angular frequency w = square root of (k/m).
Yes, it is one of the two equivalent definitions of SHM. A motion is simple harmonic if its displacement follows x = A*cos(wt + phi) OR if its restoring force follows F = -kx. Both describe the same motion.
A restoring force is a force that always acts to bring the particle back toward its mean or equilibrium position. In SHM this force is F = -kx, and the minus sign shows it is always opposite to the displacement.
Since k = m*w^2, the time period is T = 2*pi * square root of (m/k). A larger mass gives a longer period, while a larger force constant k gives a shorter period.
