Spring Force and SHM

Let us cosider the force exerted on a mass by a spring attached to it.

This force take the form F = - k X

Where X measures the displacement of the mass from an equilibrium position;

k is a constant characteristic of the particular spring known as spring constant.

This force law is known as Hooke's law.

This Java applet let you familar with this kind of relation and simple harmonic motion。

How to play:

There is a spring on the table, a string is connected to the spring over a light frictionless pulley.

You can attach mass/blocks to the spring :

1. Move the mouse button with the blocks
2. The color of those blocks above the mouse pointer will turn black.
3. Click the mouse button to attach those black blocks to the spring.
4. The mass of those attached blocks will be shown near another spring (to the right).

The spring will relax to its equilibrium position.

You can detach mass/blocks from the spring

1. Move the mouse button within the region of the attached blocks.
2. The color of those blocks below the mouse pointer will turn black.
3. Click the left mouse button to dettach those black blocks to the spring.
4. If you click the right mouse button and drag it up/down,
the force exerted on the spring will not balance the weight of the mass.
It will starts to oscillate in simple harmonic oscillation (SHM)

Press the mouse button to suspend the animation, click it again to resume.

Press Stop button to reset the spring back to equilibrium position.

Press Reset button to reset parameters to default values.

	X-axis	Y-axis
blue dots	displacement	Force
red dots	displacement	Velocity

Exercises：

1. Find out the spring-constant?
2. Green dot is the equilibrium position. How to determine the smpiltude of the oscillation?
3. Measure the peroid of the oscillation. What is the relation between mass and the period?
4. What else did you find out?

If a spring with a mass attached to it is slightly stretched or compressed and then let loose,

it will oscillate in a way close resembling (simple harmonic motion SHM).

Many elastic systems (building, flagpoles, airplane wings, etc) behave in a very similar fashion.

Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw

Author：Fu-Kwun Hwang, (Click for more than 40 physics related java applets)

Dept. of physics, National Taiwan Normal University

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