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