7) A spring has is stretched horizontally to the right from a wall 0.5 meters by...

7) A spring has is stretched horizontally to the right from a wall 0.5 meters by a force of 40 newtons. This spring has a mass of 10 kg. The mass is pulled to the right (from the equilibrium position) 1 meter and released (at t = 0) with an initial velocity to the right of 2 meters per second.

I) Write down the differential equation that governs the motion of the mass. Include the initial conditions. (assume no damping).

II) Find the position of the mass as a function of t for all t ≥ 0.

III) Write the solution in the form x(t) = A cos(ωt - δ)

IV) Suppose a damping device is attached to the mass-spring system with the magnitude of the damping force equal to c timesthe speed of the mass. For which values of c is the system over damped?

Solutions

Expert Solution

Harmonic motion of a spring mass system. For an assumed damping force, proportional to velocity calculation of the constant of proportionality for which the system is overdamped.

genius_generous answered 1 year ago

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