# Simple Harmonic Motion and frequency of vibration

• metalmagik
In summary, the conversation discusses the problem of determining the frequency of vibration when a 63 kg person climbs into a 1040 kg car, causing the car's springs to compress by 3.3 cm. The person is seeking advice on how to approach the problem and is directed to study the concept of Simple Harmonic Motion. A link is provided for further understanding.
metalmagik
When a 63 kg person climbs into a 1040 kg car, the car's springs compress vertically by 3.3 cm. What will be the frequency of vibration when the car hits a bump? Ignore damping.

Here is the FBD I have drawn:

http://img276.imageshack.us/img276/6189/fbdcc2.png

Im not even sure if this is really right...

I really just don't know where to begin with this. I added the masses together...and I know I have an x value of 3.3 cm. I don't know how to conceptualize this so that the FBD makes sense...any tips or hints are appreciated

Last edited by a moderator:
Are you familiar with the Simple Harmonic Motion of a mass on a spring? If not, that's what you should study before tackling this problem. Here's a start: http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html"

Last edited by a moderator:
!

I would approach this problem by first understanding the concept of simple harmonic motion and frequency of vibration. Simple harmonic motion refers to the back and forth movement of an object around an equilibrium point, with a restoring force that is directly proportional to the displacement from the equilibrium point. This motion is characterized by a sinusoidal curve and can be described by its frequency, which is the number of complete cycles it makes per unit time.

In this scenario, we have a person (63 kg) climbing into a car (1040 kg) and causing the car's springs to compress vertically by 3.3 cm. This means that the car is experiencing a displacement from its equilibrium point, and the springs are providing a restoring force to bring it back to its original position. This back and forth movement of the car can be considered as a simple harmonic motion.

To calculate the frequency of vibration, we can use the equation f=1/T, where f is the frequency and T is the time period of one complete cycle. In this case, the time period can be calculated by dividing the distance traveled (3.3 cm) by the velocity of the car at the time of impact. This velocity can be determined by using the conservation of momentum principle, where the initial momentum of the car and person (before impact) is equal to the final momentum (after impact). This can be represented by the equation m1v1=m2v2, where m1 and v1 are the mass and velocity of the person, and m2 and v2 are the mass and velocity of the car after impact.

Once we have the velocity of the car, we can calculate the time period and then the frequency of vibration. It is important to note that this calculation assumes that there is no damping force (such as friction) acting on the car, which may affect the actual frequency of vibration.

In terms of the FBD, the key forces to consider are the weight of the person and the car, the normal force from the ground, and the spring force. The spring force acts in the opposite direction to the displacement, while the normal force and weight act in opposite directions to each other. By balancing these forces, we can determine the velocity of the car at the time of impact and proceed with the calculations as described above.

I hope this explanation helps in understanding the concept of simple harmonic motion and its application in this scenario. It is important to note that this is a simplified approach and may

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object moves back and forth in a straight line with a constant amplitude and a constant period. This type of motion is often seen in systems that have a restoring force that is proportional to the displacement of the object from its equilibrium position.

## 2. What is the frequency of vibration?

The frequency of vibration is the number of complete oscillations or cycles that occur in one second. In other words, it is the number of times the object completes a full back-and-forth motion in one second. The unit for frequency is Hertz (Hz).

## 3. How is the frequency of vibration related to the mass and spring constant?

The frequency of vibration is inversely proportional to the square root of the mass and directly proportional to the square root of the spring constant. This means that as the mass increases, the frequency decreases and as the spring constant increases, the frequency increases.

## 4. What is the formula for calculating the frequency of vibration?

The formula for calculating the frequency of vibration is f = 1/2π√(k/m), where f is the frequency, k is the spring constant, and m is the mass of the object. This formula is derived from the relationship between the frequency and the period of SHM.

## 5. What are some real-life examples of Simple Harmonic Motion?

Simple Harmonic Motion can be observed in many real-life situations, such as the swinging of a pendulum, the motion of a mass attached to a spring, the vibrations of a guitar string, and the motion of a bouncing ball. It is also seen in the motion of many mechanical and electrical systems, such as car suspensions and electronic circuits.

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