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Consider a mass-spring system with an iron ball (weight 16 pound force) that stretches 8/9 ft...

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Advance Math

Consider a mass-spring system with an iron ball (weight 16 poundforce) that stretches 8/9 ft with undamped motion. The spring isinitially displaced 6 inches upwards from its equilibrium positionand given an initial velocity of 1 ft/s downward. Assume therelation mg=hk.

a. Find the displacement at any time t.

b. Find the natural frequency of the mass-spring (i.e. ironball-spring) system.

c. How many cycles per minutes will the system execute?

d. What would be the amplitude and phase shift?

e. What will its motion be at t= 10 seconds if we pull the balldown from rest by 1.5ft and let it start with zero initialvelocity?

d. Now examine two cases with a damping factor of 12 lb/sec and75 lb/sec with same initial conditions.

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