The governing differential equation for a spring-mass system is given below. Initial x (0) = 2 and dx/dt (0) = 0 conditions are: * + 2 x +5x = 0 a) Find the solution to the differential equation, considering the initial conditions. b) When is the displacement zero for the first time? c) How many complete oscillation cycles will take place in thirty seconds?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.