5. A mass weighing 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10 sin(t/2) N (newtons), and it moves in a medium that imparts a viscous force of 2 N when the speed of the mass is 4 cm/sec. Finally, the mass is set in motion from its equilibrium position with an initial downward velocity of 3 cm/sec. (a) Calculate k and ?. Remember that ? ? 0. (b) Set up the initial value problem (differential equation plus initial conditions) for u(t), the position of the mass at time t. Do not solve for u(t).
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Mathematically, this can be expressed as: F = -kx where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. In this case, we are given that the mass weighs 5 kg and stretches the spring by 10 Show more…
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