a) 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 ?
b) 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 1 in a manner that is directly determined by that quantity itself (as opposed to being directly determined by time).
You can draw this situation from your imagination, from familiar scientific phenomena or from daily life from anywhere as long as the scenario is clearly described and convincingly fits with the required relationship