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Start with Newton's Law of Gravitation: F=(GMm)/R^2 (1) Since orbits are assumed to be circular recall the equation for centripetal force: F=(mv^2)/R (2) We can now equate these 2 forces due to them being...

The 2 in front of the x^2 can cause confusion. In this case, the equation can be divided through by 2, to produce x^2+2x-3=0. From here it can be factorised by working out what adds to make '2' and times ...

The acceleration or unbalanced force is proportional to the displacement of the object from its equilibrium position and acts in the opposite direction

Mathematically, this may be expressed as a=-...

Electric current is a measure of the rate of flow of charges. What this means is how many charges are flowing in a circuit in a certain time period. Mathematically this is expressed as I=Q/t where I is fo...

Firstly we would differentiate each equation with respect to t to find dx/dt and dy/dt- which gives us dx/dt=t and dy/dt=-4t^-2. Once you have found these you must divide dy/dt by dx/dt (or dy/dt x dt/dx)...