B) If a simple planar pendulum seems to be a simple harmonic oscillator, and if

Question

B) If a simple planar pendulum seems to be a simple harmonic oscillator, and if a simple harmonic oscillator is a system that acts like a mass on a spring, then why is the period of a mass on a spring independent of spring length ?

C) Describe an entirely different scenario in which the time - rate of change of some variable is a function of that variable itself. Ideally, you might come up with a situation in which it is the rate of change of the rate of change (i.e.: the second derivative) that is relevant and in which the function at hand is a linear function, but neither of these two features is mandatory. Somehow or another in words and pictures, capture a situation in which some quantity changes as time passes

Explanation / Answer

c) according to the definition of simple harmonic motion , a motion is simple harmonic when the acceleration is always directed towards a fixed point and its magnitude is propotional to the displacement of the particle from this point. hence the period in simple harmonic motion is independent of the length.

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