Designers are testing a new idea for an amusement ride. The design is basically a large platform that is on vertical sliders and connected to a spring. The system is subjected to an initial displacement then released. If the designers are not careful, the ride may be to dangerous to use.

What is known:

mass m = 1,000 slugs

spring constant k = 5,000 or 10,000 lb/ft

initial displacement y(0) = -20 ft

initial velocity y(0) = 0 ft/s

Question

What is the maximum acceleration the occupants will undergo during the ride?

Approach

Model the ride as a spring-mass system.

Displace the system from its equilibrium position.

Draw a free-body diagram.

Determine the differential equation of motion using F = ma.

Solve the equation of motion for the displacement.

Differentiate with respect to time twice to get the acceleration equation.

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