Physics - Online Test

The damped natural frequency fd is related to the natural frequency fn by a  relation 

 fd=fn1−ζ2−−−−−√

where damping ratio ζ  is <= 1 

so the fd is less than the natural frequency 

When a satellite revolves around a planet in its orbit, it possesses both potential energy (due to its position against the gravitational pull of earth) and kinetic energy (due to orbital motion).

∴Total Energy = Potential Energy(U) + Kinetic Energy(K) = −GMmr+GMm2r = −GMm2r=−L22mr2

Hence we can say that total energy of circularly orbiting satellite is negative.

instantaneous acceleration is measured over a "short" time interval. The word short in this context means infinitely small or infinitesimal — having no duration or extent whatsoever.

It's a mathematical ideal that can can only be realized as a limit. The limit of a rate as the denominator approaches zero is called a derivative.

Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero — or alternatively, acceleration is the derivative of velocity.

a=limt→0ΔvΔt=dvdt

e=−M(didt)

M is mutual inductance