Vertical Oscillation assuming no damping

AI Thread Summary
To determine the frequency of vertical oscillation for a car and passenger system, the effective spring constant must be calculated using the displacement caused by the added mass. The 4.5 cm sink indicates the system's response to the combined weight of the 85-kg person and the 300-kg car. The equations for angular frequency (ω) and frequency (f) are essential, with ω being derived from the spring constant (k) and total mass (m). The discussion highlights confusion regarding the amplitude and the relationship between displacement and spring stiffness. Ultimately, understanding these relationships is crucial for solving the problem accurately.
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Homework Statement


An 85-kg person steps into an experimental car of mass 300 kg, causing it to sink 4.5 cm on its springs. If started into vertical oscillation, and assuming no damping, at what frequency will the car and passenger vibrate on these springs.


Homework Equations


ω=√k/m
ω=2πf
x(t)=Acos(ωt)

The Attempt at a Solution


I thought 4.5 would be the amplitude of the oscillation but then I had 3 unknowns, the distance traveled, omega, and the time. Then I thought it may be the distance traveled and the amplitude would be 4.5/2 but I ended up stuck again.
 
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The amount of sink and the mass of the person are related via the stiffness of the springs.
 
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