Vertical Oscillation assuming no damping

The frequency of oscillation is determined by the stiffness and the mass of the system.In summary, the 85-kg person stepping into the 300 kg car causes it to sink 4.5 cm on its springs. The frequency of oscillation of the car and passenger on these springs can be calculated using the formula ω=√k/m, where ω is the angular frequency, k is the stiffness of the springs, and m is the combined mass of the car and the person. Alternatively, the frequency can also be calculated using the formula ω=2πf, where f is the frequency in Hertz, and x(t)=Acos(ωt) represents the displacement of the car and passenger over time.
  • #1
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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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  • #2
The amount of sink and the mass of the person are related via the stiffness of the springs.
 

1. What is vertical oscillation?

Vertical oscillation is the up and down movement of an object or system about a fixed point or equilibrium position. It is caused by the force of gravity acting on the object or system.

2. How is vertical oscillation measured?

Vertical oscillation is measured by the amplitude, which is the distance between the highest and lowest points of the oscillation, and the frequency, which is the number of oscillations per unit time.

3. What is the difference between vertical oscillation and vertical vibration?

Vertical oscillation refers to the natural movement of an object or system, while vertical vibration is the result of an external force or disturbance acting on the object or system.

4. What is the effect of damping on vertical oscillation?

Assuming no damping, the amplitude of the oscillation will remain constant. However, if damping is present, the amplitude will decrease over time due to the dissipation of energy.

5. How can vertical oscillation be applied in real-world situations?

Vertical oscillation can be seen in various natural phenomena such as the motion of a pendulum or the movement of ocean waves. It is also used in engineering and construction to design structures that can withstand vertical oscillations caused by earthquakes or wind loads.

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