Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealized oscillation. Practically all the oscillations that one can see directly in the natural world are much more complicated than SHM. Why then do physicists make such a big deal out of studying SHM?

It is the only kind of oscillation that can be described mathematically

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Any real oscillation can be analysed as a superposition (sum or integral) of SHMs with different frequencies

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Physics is concerned mainly with the unnatural world.

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Students are too stupid to appreciate the real world.

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Solution

The correct option is B Any real oscillation can be analysed as a superposition (sum or integral) of SHMs with different frequencies
Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis. Here any waveform can be represented as closely as desired by the combination of a sufficiently large number of sinusoidal waves that form a harmonic series. Fourier's theorem suggests that any periodic function can be represented as an algebraic sum of sine and cosine functions called a Fourier Series.

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Q. Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealized oscillation. A simple harmonic oscillation has

Q. The oscillators that can be described in terms of sine or cosine functions are called

Q. Which physical quantity oscillates with the same frequency as that of SHM for a harmonic oscillator?

Answer the following questions:

(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than. Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?

(d) What is the frequency of oscillation of a simple pendulum mounted in a cabinthat is freely falling under gravity?

Q. Answer the following questions :
(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:

T = 2 π \sqrt{\frac{m}{k}}

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angle of oscillation a more involved analysis shows that T is greater than

2 π \sqrt{\frac{l}{g}}

. Think of a qualitative argument to appreciate this result.
(c) A man with a wristwatch on his hand falls from the top of a tower. Does the
watch give correct time during the free fall ?
(d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity ?

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