Physics · Oscillations · NEET
No, not strictly. In pure SHM the amplitude stays constant forever, but in a damped oscillation the amplitude falls with time as A e^(-bt/2m). NCERT says damped SHM is only approximately simple harmonic, and only for time intervals much shorter than 2m/b. So over a short time it looks like SHM, but over long time the shrinking amplitude makes it non-SHM.
Because a resistive (damping) force acts opposite to the motion. This force does negative work on the body, so mechanical energy is slowly changed into heat. Less energy means smaller swings. The amplitude at time t is A e^(-bt/2m): the exponential term is always less than 1 and keeps falling, so the amplitude keeps shrinking.
The damping force is taken as F = -b v, so b is the constant that links the resistive force to the speed v. A larger b means a stronger resistive force and faster loss of amplitude. The unit of b is kg per second (N per (m/s)). It appears in the amplitude term e^(-bt/2m) and in the damped frequency w'.
Yes, a little. The damped angular frequency is w' = root(k/m - (b/2m)^2), which is slightly less than the natural frequency w0 = root(k/m). So the damped time period is slightly longer than the undamped one. For light (weak) damping, b is small and w' is almost equal to w0, so the change is often ignored in easy problems.
The total mechanical energy falls with time because energy leaks out as heat. For weak damping the energy at time t is about E(t) = E0 e^(-bt/m). Notice the energy has e^(-bt/m) while the amplitude has e^(-bt/2m); this is because energy is proportional to amplitude squared, so its exponent is doubled.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
x(t) = A e^(-bt/2m) cos(w't + phi), where A e^(-bt/2m) is the amplitude that shrinks with time, b is the damping constant, m is the mass, and w' = root(k/m - (b/2m)^2) is the damped angular frequency.
A car shock absorber, a swing left alone, a pendulum swinging in air, or a tuning fork whose sound slowly fades. In each case a resistive force removes energy and the swings get smaller.
In damped oscillations no outside push is given, so amplitude keeps falling. In forced oscillations an external periodic force is applied again and again to keep the motion going; if its frequency matches the natural frequency, resonance occurs. Read the next concept, Forced Oscillations and Resonance, for more.
No. The amplitude is A e^(-bt/2m), which keeps decreasing with time. Only in undamped (ideal) SHM does the amplitude stay constant.
For weak damping, energy falls as E(t) = E0 e^(-bt/m). Because energy is proportional to amplitude squared, its exponent (bt/m) is twice that of the amplitude (bt/2m).
