A gasket that seals fuel reservoirs for the space shuttle can be modeled by the following differential Equation:
m*d^2y/dt^2 + h*dy/dt + Ky = u
u is input force coming from external vibrations during flight
m=10000 kg is the inertia of the reservoir+gasket system
K=250N/m is the elasticity of the gasket material
y is position of system
h depends linearly on the ambient temperature
h(T)= 0.09+0.0025T
Where T is the external temperature in fahrenheit degrees.
During takeoff, the reservoirs undergo strong vibrations that can be modeled as sinusoidal inputs
Determine the system natural frequency and damping ratio
Write transfer function