"il 64% 11:37 PM Tutorial 16-04-2021.docx 1. Solve by variation of parameter method. y "+4y = sin? 2t 2. Solve by undetermined coefficient method. y"-6y'+25 y = 2 sin -a t - Cos 2 2 3. A steel ball weighing 128 lb is suspended from a spring, whereupon the spring is stretched 2 ft from its natural length. The ball is started in motion with no initial velocity by displacing it 6 in above the equilibrium position. Assuming no air resistance, find (a) an expression for the position of the ball at any time t, and (b) the position of the ball at t = sec. 12 4. Find the distance at any time of a periodic oscillations of a damped mass-and-spring system with m= 1,c= 2, and k = 26under the influence of an external force F(t) =82cos 4t with x(0) = 6 and x'(0) = 0.

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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.