Write the differential equation needed to solve the problem, but do not solve.
A 1 kg mass is suspended from a spring in a viscous fluid that provides
resistance of 8 N for every m/s of velocity. The spring (outside of the fluid)
is stretched 0.5 m by a force of 2 N. If the spring is set in motion 0.5 m above
equilibrium at a velocity of 3 m/s downward, what is the position of the mass at
any time t?

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Write the differential equation needed to solve the problem, but do not solve.
A 4 kg mass is suspended from a spring with spring constant 16 N/m. A battery is
attached to the system which provides a force of 3cos(2t) N. If the spring is
set in motion from equilibrium at a velocity of 3 m/s upward, what is the
position of the mass at any time t?

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