Oscillating table and reference frames

In summary, the problem involves a horizontal table oscillating with an amplitude vector A and angular frequency ω, and a block sitting on the table with mass m and linear friction resulting in a force F = −λu. The task is to derive the equations of motion for the block in the frame of reference of the table, using axes (ξ , η, ζ ) parallel to the axes (x, y, z ) in the inertial frame. The equations can be derived using Newton's second law of motion, F = ma, and substituting for the given force and incorporating the displacement and angular frequency.
  • #1
Mathmos6
81
0

Homework Statement



A horizontal table oscillates with a displacement A sin ωt , where A = (Ax , 0, Az ) is the amplitude vector and ω the angular frequency in an inertial frame of reference with the z axis vertically upwards, normal to the table. A block sitting on the table has mass m and linear friction that results in a force F = −λu, where λ is a constant and u is the velocity difference between the block and the table. Derive the equations of motion for this block in the frame of reference of the table using axes (ξ , η, ζ ) on the table parallel to the axes (x, y, z ) in the inertial frame.

Can someone please help me just derive the equations of motion, so I can continue with the later parts of the question? I'm stuck! :(
 
Physics news on Phys.org
  • #2
Homework Equations F = maThe Attempt at a Solution I have tried to use Newton's second law of motion, F = ma, and substitute for the force given in the question, but I'm not sure how to incorporate the displacement and angular frequency.
 

Related to Oscillating table and reference frames

1. What is an oscillating table and how does it work?

An oscillating table is a scientific instrument that is used to study the movement of objects in a specific reference frame. It consists of a flat surface that can move back and forth, creating a repetitive motion. This motion can be controlled and adjusted to simulate different types of oscillatory movements.

2. What is the purpose of using an oscillating table in research?

Oscillating tables are commonly used in scientific research to study the effects of oscillatory motion on various objects. They can also be used to test the stability and resilience of structures and materials under different types of vibrations. In addition, oscillating tables can be used to investigate the dynamics of different systems and their response to external forces.

3. How is the reference frame of an oscillating table determined?

The reference frame of an oscillating table is determined by its motion. The center of the table is usually considered as the origin of the reference frame, and the direction of the oscillation is used to define the positive and negative axes. In some cases, the reference frame may also be defined by the position of the object being tested.

4. Can an oscillating table be used to simulate real-life situations?

Yes, an oscillating table can be used to simulate real-life situations, such as earthquakes, vibrations in buildings, and vehicle collisions. By adjusting the frequency and amplitude of the oscillations, researchers can recreate different types of vibrations and study their effects on objects and structures.

5. Are there different types of oscillating tables?

Yes, there are various types of oscillating tables, each designed for a specific purpose. Some common types include single-axis tables, multi-axis tables, and shaker tables. The type and design of the table may vary depending on the type of research being conducted and the desired parameters of motion.

Similar threads

I Using reference frames for derivation of Lagrangian
    • Mechanics
Replies
25
Views
1K
Position of particle in inertial reference frame
    • Introductory Physics Homework Help
Replies
3
Views
1K
Foucault Pendulum at the North Pole
    • Introductory Physics Homework Help
Replies
9
Views
791
Precession of Rotating Rigid Body from Two Different Frames
    • Advanced Physics Homework Help
Replies
2
Views
1K
I Principle of relativity and Galileo's group
    • Classical Physics
Replies
10
Views
998
Frame of reference (non inertial/inertial) in an Atwood Mach
    • Introductory Physics Homework Help
Replies
13
Views
2K
Motion in a Rotating Reference Frame
    • Advanced Physics Homework Help
Replies
1
Views
2K
Finding the force of constraint--compound pendulum on spring
    • Advanced Physics Homework Help
Replies
1
Views
2K
Inertial/non-inertial reference frames
    • Advanced Physics Homework Help
Replies
8
Views
3K
I Non-Newtonian description of an accelerated object
    • Mechanics
Replies
8
Views
845

Hot Threads

Recent Insights

Back
Top