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A spring is stretched 40 cm by a mass of 3 kg, and the mass is attached to a viscous damper that exerts a force of 4 N when the velocity of the mass is 2 m/s. (a) ( Find the differential equation that characterizes u(t), the displacement of the mass from equilibrium at time t, when it is set in motion. Be sure to specify the units that you are using and show how you find the parameters in the equation. You do not need to solve the equation here. (b) Find a fundamental pair of solutions for the equation you found in (a). (c) The mass is pulled down 30 cm from equilibrium and then thrust downwards with an initial speed of 3 m/s. Find u(t).

A spring is stretched 40 cm by a mass of 3 kg, and the mass is attached to a viscous damper that exerts a force of 4 N when the velocity of the mass is 2 m/s. (a) ( Find the differential equation that characterizes u(t), the displacement of the mass from equilibrium at time t, when it is set in motion. Be sure to specify the units that you are using and show how you find the parameters in the equation. You do not need to solve the equation here. (b) Find a fundamental pair of solutions for the equation you found in (a). (c) The mass is pulled down 30 cm from equilibrium and then thrust downwards with an initial speed of 3 m/s. Find u(t).

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A spring is stretched 40 cm by a mass of 3 kg, and the mass is attached to a viscous damper that exerts a force of 4 N when the velocity of the mass is 2 m/s. Find the differential equation that characterizes u(t), the (a) displacement of the mass from equilibrium at time t, when it is set in motion. Be sure to specify the units that you are using and show how you find the parameters in the equation. You do not need to solve the equation here. (Б) Find a fundamental pair of solutions for the equation you found in (a). (c) The mass is pulled down 30 cm from equilibrium and then thrust downwards with an initial speed of 3 m/s. Find u(t).
Transcribed Image Text:A spring is stretched 40 cm by a mass of 3 kg, and the mass is attached to a viscous damper that exerts a force of 4 N when the velocity of the mass is 2 m/s. Find the differential equation that characterizes u(t), the (a) displacement of the mass from equilibrium at time t, when it is set in motion. Be sure to specify the units that you are using and show how you find the parameters in the equation. You do not need to solve the equation here. (Б) Find a fundamental pair of solutions for the equation you found in (a). (c) The mass is pulled down 30 cm from equilibrium and then thrust downwards with an initial speed of 3 m/s. Find u(t).
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