What Are the Key Factors in Solving Mechanical Vibration Problems?

In summary, the conversation discusses solving a problem involving a weight stretching a spring with given conditions. The main objective is to find the maximum amplitude, time it reaches its highest point, and maximum velocity. The governing equation for this problem is m\ddot{y} + ky = 0, representing simple harmonic motion. The initial condition provided is the starting point for solving the equation and determining the arbitrary constants.
  • #1
s7b
26
0
Hi,

I don't understand how to go about solving a problem like this;

A weight stretches a spring 3 inches. It is set in motion at a point 4 inches below it's equilibrium point with zero velocity.

-Find the maximum amplitude
-When does it reach (the first time) it's highest point
-Find it's maximum velocity
 
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  • #2
Your governing equation will be
[tex]m\ddot{y} + ky = 0[/tex]
which is a simple harmonic motion

s7b said:
Hi,
A weight stretches a spring 3 inches.

This will allowed you to compute k/m.


s7b said:
Hi,

It is set in motion at a point 4 inches below it's equilibrium point with zero velocity.
This is the initial condition which will allowed you to determined the arbitrary constants when solving the governing equation.
 

Related to What Are the Key Factors in Solving Mechanical Vibration Problems?

What is mechanical vibration?

Mechanical vibration is the back and forth motion of an object or system due to an external force or disturbance. It can occur in various forms, such as oscillation, pulsation, or resonance.

What causes mechanical vibrations?

Mechanical vibrations can be caused by a variety of factors, including external forces, such as wind or earthquakes, or internal forces, such as rotating machinery or structural imperfections. They can also be induced by periodic or random disturbances.

How do mechanical vibrations affect structures?

Mechanical vibrations can have both positive and negative effects on structures. On one hand, they can cause fatigue and damage to structures, especially if they occur at resonance frequencies. On the other hand, they can also be harnessed for useful purposes, such as in musical instruments, engines, and other mechanical systems.

How are mechanical vibrations measured?

Mechanical vibrations can be measured using various instruments, such as accelerometers, which measure the acceleration of an object, and vibrometers, which measure the velocity or displacement of an object. These measurements are typically recorded as a function of time and can provide valuable information about the frequency, amplitude, and phase of the vibrations.

How can mechanical vibrations be controlled or reduced?

There are several methods for controlling or reducing mechanical vibrations, depending on the specific situation. These can include adding damping materials to the structure, changing the mass or stiffness of the structure, or implementing active control systems, such as vibration absorbers or isolators. It is also important to identify and address the root cause of the vibrations to prevent them from occurring in the first place.

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