A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.

A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.
a) Specify the differential equation as an IVP which describes the above mass-spring system.
b) Solve the above IVP to find the position of the mass at any later time.
c) Determine the period and amplitude of the motion described by the above system.


Solution:
A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.

A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.

A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.

A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from equilibrium position with a downward velocity 2 ft/s.


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