An automobile exhibits a vertical oscillating displacement o

An automobile exhibits a vertical oscillating displacement of maximum amplitude 5 cm and a measured maximum acceleration of 2000 cm/s2. Assuming the automobile can be modeled as a single-degree-of-freedom system in vertical direction, calculate automobile natural frequency. 20 rads/s

Solution

there is no damper in the circuit.

Hence the equation can be written as

m x(2dot) (t) + kx (t) = 0

The peak velocity = w_n A and peak acceleration = w_n² A where A is the displacement

therfore 2000 cm/sec² = w_n²   x 5cm therefore  w_n²  = 2000/5 = 400

hence w_n = sqrt (400) = 20rad/sec