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# (1 point) Consider a spring attached to a 1 kg mass, damping constant 6 = 9,...

(1 point) Consider a spring attached to a 1 kg mass, damping constant 6 = 9, and spring constant k = 20. The initial position of the spring is -1 metres beyond its resting length, and the initial velocity is 2 m/s. After 1 second, a constant force of 60 Newtons is applied to the system for exactly 2 seconds. Set up a differential equation for the position of the spring y (in metres beyond its resting length) after t seconds: Denote the unit step function un(t) by un (ie, us(t) would be u5). y"9 y20 y 60(u1-u3) 1 Take the Laplace transform of both sides of the given differential equation. Denote the Laplace transform of y(s) by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). tA2Y+9tY+20Y+t-11

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