Mechanical vibrations homeworks

In summary, to find the distance x from the axis of variation O for a 1 kg slider in a system with an oscillation period of 0.9 s, we can use the equation I\varphi(over letter "..")+k\varphi=0, where I represents the moment of inertia of the system containing the unknown distance x. By putting the equation in the correct form, the frequency of vibration can be identified and then x can be calculated to achieve the desired period.
  • #1
leocer
1
0

Homework Statement



1.png


what distance x from the axis of variation O should be 1 kg
slider, the system oscillations period is 0.9 s?

T=0.9 s;
the spring stiffness k=75 N/m;
slider mass m=1 kg;
beam mass m=3 kg;

Homework Equations


I[itex]\varphi[/itex](over letter "..")+k[itex]\varphi[/itex]=0
[itex]\varphi[/itex](over letter "..")+[itex]\omega[/itex]^2[itex]\varphi[/itex]=0


The Attempt at a Solution



I have no solution. Please help me to find solution. Thanks.
 
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  • #2
Can you write the ordinary differential equation that describes the system in terms of rotational moment of inertia, time, spring constant, and dimenions? The moment of inertia of the system will contain an unknown distance x. Once you put the ODE in correct form, you can identify the frequency of vibration. It will contain x. Then find x such that you get the period you seek.
 

Related to Mechanical vibrations homeworks

1. What is the purpose of studying mechanical vibrations?

The study of mechanical vibrations is important for understanding the behavior of mechanical systems, such as machines and structures. It allows us to predict and analyze the response of these systems to external forces and disturbances, and to design them for optimum performance and safety.

2. What are some common types of mechanical vibrations?

There are three main types of mechanical vibrations: free vibrations, forced vibrations, and self-excited vibrations. Free vibrations occur when a system is disturbed and left to vibrate on its own, while forced vibrations are caused by an external force or motion. Self-excited vibrations are those that arise due to internal sources, such as friction or aerodynamic forces.

3. How are mechanical vibrations measured?

Mechanical vibrations can be measured using various instruments, such as accelerometers, which measure the acceleration of a vibrating object, or displacement transducers, which measure the displacement or position of the object. These measurements can then be used to calculate other parameters, such as velocity and frequency.

4. What are some real-world applications of mechanical vibrations?

Mechanical vibrations have a wide range of applications in various industries, including automotive, aerospace, and civil engineering. They are used to design and optimize machinery and structures, as well as to diagnose and troubleshoot problems in these systems. Vibrations are also important in fields such as acoustics and seismology.

5. How can mechanical vibrations be controlled?

There are several methods for controlling mechanical vibrations, including using vibration isolators or dampers to reduce the transmission of vibrations from one part of a system to another. Designing systems with proper stiffness and damping can also help to minimize vibrations. Active control techniques, such as using feedback control systems, can also be employed to reduce or eliminate vibrations in certain situations.

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