Solving Mass Spring System with Horizontal Force Applied

In summary, the conversation is about a mechanics assignment involving a mass attached to a vertical wall by a spring and dampner. A horizontal force is applied to the mass, which has a weight of 0.1kg, a spring stiffness of 0.6N/m, and a damping constant of 0.5 Ns/m. The task is to find the second order differential equation that governs the motion of the mass, and the individual is looking for help on where to start. They are asked to write out the equation of motion without the damping term, and then add the damping term.
  • #1
Billybobbean
2
0
Hello PF users! This is my first post here, I'm looking for a bit of help with my mechanics assignment.

1. The question is asking me to investigate a mass with a spring and dampner attaching it to a vertical wall, and then it having a horizontal force applied to it.
The mass is 0.1kg
The springs stiffness is 0.6N/m
and there is a dampner with a damping constant of 0.5 Ns/m
At time=0 the mass is in its stationary equilibirum position when it has a force of 0.1sin(t) N applied to it (away from the wall, i.e. the spring will stretch)

2. I am then asked to find the second order differential equation that governs the subsequent motion, which is what I'm stuck on. When I say stuck on I mean don't really know where to start.

3. Sorry, I got nothing :frown:

Any help/pointers/explanations you can give would be helpful, at the moment I am completely stumped.
 
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  • #2
Billybobbean said:
2. I am then asked to find the second order differential equation that governs the subsequent motion, which is what I'm stuck on. When I say stuck on I mean don't really know where to start.
Can you write out the equation of motion without the damping term? (hint: acceleration is the second derivative of position with respect to time). That is a second order differential equation. Then add the damping term.

AM
 
  • #3
cant make the forum code work ill draw it when i get home.
 
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FAQ: Solving Mass Spring System with Horizontal Force Applied

1. What is a mass spring system with horizontal force applied?

A mass spring system with horizontal force applied is a physical system that consists of a mass attached to a spring, with a horizontal force being applied to the mass. This system is commonly used in physics experiments to demonstrate the principles of simple harmonic motion and to study the effects of different forces on the motion of the mass.

2. How do you solve a mass spring system with horizontal force applied?

To solve a mass spring system with horizontal force applied, you can use the equation F = ma, where F is the applied force, m is the mass of the object, and a is the acceleration of the object. You can also use the equation F = -kx, where k is the spring constant and x is the displacement of the mass from its equilibrium position. By setting these two equations equal to each other, you can find the acceleration of the mass and determine its motion over time.

3. What factors affect the motion of a mass spring system with horizontal force applied?

The motion of a mass spring system with horizontal force applied is affected by several factors, including the mass of the object, the stiffness of the spring, the magnitude and direction of the applied force, and any external forces or friction acting on the mass. These factors can alter the acceleration and displacement of the mass, leading to different types of motion such as simple harmonic motion or damped oscillations.

4. How does the amplitude of the motion change with different horizontal forces?

The amplitude of the motion in a mass spring system with horizontal force applied depends on the magnitude of the applied force. As the applied force increases, the amplitude of the motion also increases, resulting in a larger displacement of the mass from its equilibrium position. However, if the applied force is too large, the system may exceed its elastic limit and the spring may become permanently deformed.

5. What happens to the motion of the mass spring system when the applied force is removed?

When the applied force is removed from a mass spring system, the mass will continue to oscillate back and forth due to its inertia and the energy stored in the spring. The amplitude of the motion will gradually decrease due to the effects of friction and damping. Eventually, the mass will come to rest at its equilibrium position and the system will return to a state of static equilibrium.

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