Simple Harmonic Motion and Resonance

In summary, a car with a mass of 1220kg, including the driver, travels over a bridge with expansion gaps spaced 5.5m apart at a speed of 12.0m/s. When two more 80kg passengers are added to the car, the maximum oscillation amplitude is reached at a certain speed. The car's suspension experiences sag when the two passengers are added. The car's suspension exhibits SHM in the vertical direction, resulting in periodic bumps when driving over the expansion gaps. The time elapsed between these bumps and the periodic pushing of a vibrating body are important factors in understanding the car's oscillation behavior.
  • #1
Gyoung68
1
0

Homework Statement


A car with mass 1220kg including the driver travels over a bridge with expansion gaps spaced 5.5m apart. At a speed of 12.0m/s, the car bounces up and down with exceptionally large amplitude. Two more 80kg passengers now get in the car. a) What speed will result in maximum oscillation amplitude? b) How much did the car's suspension sag with the two added passengers? c) What kind of oscillation behavior results from the car's suspension


Homework Equations


Something dealing with wavelength, wave speed, and mass


The Attempt at a Solution


Not a clue
 
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  • #2
The answer is in the title of your post. The car is suspended - on what?

http://www.carbibles.com/suspension_bible.html

So it performs SHM in vertical direction. It gets some bump whenever it drives through the expansion gaps. What is the time elapsed between these bumps? What happens when a vibrating body is pushed periodically?


ehild
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of oscillatory motion where a system or object moves back and forth around a stable equilibrium point, with a constant period and amplitude. This type of motion can be seen in pendulums, springs, and other vibrating systems.

2. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is different from other types of motion because it is a type of periodic motion, meaning the system or object repeats its motion in a regular pattern. It also follows Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the object from its equilibrium position.

3. What is resonance?

Resonance is a phenomenon that occurs when a system is subjected to an external force or frequency that matches its natural frequency. This causes the system to vibrate with a larger amplitude, and in some cases can lead to destructive vibrations if the system is not able to dissipate the energy.

4. How does resonance occur in simple harmonic motion?

In simple harmonic motion, resonance occurs when the frequency of the external force matches the natural frequency of the system. This causes the amplitude of the motion to increase, as the system absorbs more energy from the external force.

5. How is simple harmonic motion and resonance important in real-world applications?

Simple harmonic motion and resonance have many important applications in various fields such as engineering, physics, and music. Some examples include the use of pendulums in timekeeping devices, the design of suspension bridges using resonance to reduce vibrations, and the production of sound in musical instruments.

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