Ch 5Oscillations — concept-first.

Oscillation is one of the most common motions in nature, and you have already met dozens of examples without necessarily naming them as such: a cradle rocking, a child's swing, the pendulum of a clock…

Periodic motion is defined as any motion that repeats itself, in exactly the same way, after a fixed interval of time.

To build up the idea of linear S.H.M. concretely, picture a block of mass m resting on a smooth (frictionless) horizontal surface, with one end of a spring fixed to a rigid wall and the other end atta…

Having established, in section 5.3, that the restoring force in linear S.H.M. is f = -kx (Eq. 5.1), we can now combine this with Newton's second law of motion, f = ma, to get

Section 5.4 obtained the velocity-displacement relation (Eq. 5.10) by integrating the S.H.M. differential equation once. Integrating a second time gives us x directly as a function of time.

Having obtained the general displacement expression in section 5.5, we are now in a position to formally define and derive expressions for the three quantities that, between them, completely character…

Consider a particle P performing linear S.H.M. along a straight-line path MN, with O marking the centre of MN -- the mean (equilibrium) position of the particle (Fig. 5.2).

The period T of an S.H.M. is defined as the time taken by the particle to complete exactly one full oscillation. We can derive an expression for T directly from the general displacement formula.

The frequency n of an S.H.M. is defined as the number of complete oscillations performed by the particle per unit time.

The formulas derived so far assumed a single spring of force constant k. In practice, springs are often combined -- either in SERIES (one after another, forming a single chain, Fig.

Sections 5.4-5.6 built up the mathematics of linear S.H.M. from the differential equation onward. This section takes a completely different, purely GEOMETRIC route to the exact same equations, by rela…

So far we have described an S.H.M. particle's condition at any instant using its displacement x, or its velocity v, separately.

It is often clearer to SEE the periodic nature of displacement, velocity and acceleration than to read it off the equations, so this section plots all three against phase angle (equivalently, against…

What happens if a single particle is subjected to TWO different S.H.M.s at once, both having the same period and both acting along the same straight-line path (say, the x-axis), but with different amp…

A particle performing S.H.M. possesses kinetic energy at every point of its path EXCEPT the two extreme positions (where its speed, momentarily, is zero).

An IDEAL simple pendulum is defined as a heavy particle, suspended by a massless, inextensible, perfectly flexible string, from a rigid support.

A second's pendulum is defined as a simple pendulum whose period is exactly two seconds, s (so that it completes half an oscillation, and hence ticks once, every second -- historically the basis for m…

So far this chapter has dealt exclusively with LINEAR S.H.M. -- oscillation along a straight-line path.

As a concrete and important application of angular S.H.M. (section 5.13), consider a bar magnet of magnetic dipole moment , freely suspended (e.g.

Every real oscillator, left to itself, eventually stops. This happens because some resistive influence -- air resistance, friction at a support, viscous drag in a fluid, or (as in an electrical LC cir…

If an object is simply allowed to oscillate or vibrate entirely on its own -- displaced once and then left alone, with no ongoing external driving -- it does so at its own NATURAL frequency (or, for m…

Questions from official CBSE sample papers.