# Relationship between hookes law and simple harmonic motion

### Hooke’s Law and Simple Harmonic Motion

the requirements for simple harmonic motion, (3) to learn Hooke's Law, (4) to verify learn the definition of amplitude, (8) to learn the relationship between the . A special form of periodic motion is called Simple Harmonic Motion (SHM). Simple Harmonic This relationship is called Hooke's Law. If a mass is attached to a. Hooke's Law and Simple Harmonic Motion the dependence of period of oscillation on the value of mass and amplitude of motion. k) for M = kg and your value of C. What is the percent difference between them?.

Do your data confirm this expectation? The data confirms this expectation, as the period was nearly the same for each trial. Consider the value you obtained for C. The obtained value of C is 0. What is the percent difference between them?

Repeat for a value for M of 1. Is there a difference in the percent differences? If so, which is greater and why?

This is a percent difference of 6. This is a percent difference of only 0. The greater percent difference occurs at the lower weight because the weight of the spring is almost insignificant at higher weight. The proportion of the mass to the spring is so great that it has almost no effect on the calculation. Conclusion During part one of the experiment, the vertical displacement of a spring was measured as a function of force applied to it.

• Hooke's Law and Simple Harmonic Motion
• Simple harmonic motion and Hooke’s law
• Hooke’s Law and Simple Harmonic Motion

The starting position of the spring was recorded using a stretch indicator. Mass was added to the spring, and the displacement was recorded.

This was repeated with various amounts of mass. From these data, a graph of force versus displacement was plotted, and a linear fit slope revealed the spring constant. In this endeavor, the spring constant was valued at 3.

This means there was human error, most likely in terms of not being precise with the displacement readings because the recordings for the masses used were accurate.

Because such small masses were used, any error in displacement readings was augmented.

Therefore, if a weight is hung from a spring suspended from the vertical, the resulting period of oscillation would be proportional to the square root of the attached weight. Equation 6 The work done and thus the elastic potential energy, PE, can be written as: Equation 7 The potential energy of a spring will be measured in this lab.

Simple Harmonic Motion: Hooke's Law

Measure the spring constant and potential energy of a spring and confirm the relationship between the mass and oscillatory period T. Obtain a spring with a known spring constant, a stand to attach the spring to, at least 5 weights of varying masses that can be attached to the spring, a meter stick, and a stopwatch. Secure the stand to a solid foundation and attach the spring to the stand. Make sure that there is enough room below the spring for it to stretch without hitting the table or ground.

Start with the least-massive weight. Record these values in Table 1. Measure how high above the surface of the table the spring is while in its un-stretched position. Record this displacement in Table 1. With the weight attached, slightly raise the weight before releasing it.

Observe the oscillatory motion. Measure the period T with a stopwatch. For a more accurate measurement, record the time for multiple periods and divide that time by the number of periods observed.

Do this multiple times and record the average time measured for the period T in Table 1. Calculate the potential energy of the spring for each of the different masses and record them in Table 1.

## How is simple harmonic motion related to Hooke law?

According to Equation 1, this should be linear. Fit a slope to the line. This slope will correspond to the spring constant k. Compare the measured value to the known value of the spring. Using the known spring constant and Equation 5, calculate what the period T of oscillation should be for each of the masses; report them in Table 1.

Compare them to the T that was measured with a stopwatch in step 1. Srping oscillation, Hooke's Law and the phenomenon of simple harmonic motion help in understanding the physics associated with elastic objects.

### newtonian mechanics - Hooke's Law and Simple Harmonic Motion - Physics Stack Exchange

Hooke's Law implies that in order to deform an elastic object, like a slingshot, a force must be applied to overcome the restoring force exerted by that object. Clearly the elastic object stores energy that has the potential to do work. After the work is done the elastic object undergoes oscillation. If we plot this oscillatory behavior as the object's position versus time, then the graph represents simple harmonic motion.

In this video, we will demonstrate an experiment that uses springs and weights to validate the concepts behind Hooke's law and simple harmonic motion. Before demonstrating how a spring behaves, let's revisit the concepts behind its oscillation. Imagine, applying a force to the spring, like a weight, that causes it to stretch from its initial non-deformed position until an opposing restoring force eventually balances it and equilibrium is established.

### Simple harmonic motion and Hooke’s law

Now, with the spring at its equilibrium position, if you introduce an external force and lift the attached weight to a certain height, you allow the spring to gain some elastic potential energy PE. Now when you release the spring, it undergoes a periodic motion, known as simple harmonic motion. If plotted on a graph of position versus time, the motion yields the sinusoidal waveform of simple harmonic motion.

The period of oscillation T is given by this formula, which shows that T is inversely proportional to k -- the elasticity constant, and directly proportional to m -- the mass of the weight attached.

Therefore, the larger the mass, the longer the spring would take to complete one cycle of oscillation. If this system was isolated - unaffected by external forces, the oscillations would go on indefinitely as the kinetic and potential energies, KE and PE, would be continuously converted to one another.

But in the real world there are always some frictional forces that cause damping and therefore the spring will ultimately come to a halt. Now that you have an idea about the laws that govern spring oscillation, let's see how to test them in a physics lab. This experiment consists of a spring with a known spring constant, a stand, a set of weights with different but known masses, a meter stick, and a stopwatch.

Secure the stand to a solid foundation, such as a table. Attach the spring to the stand making sure there is enough room to stretch the spring without contacting the top of the table. Using the meter stick, note the non-deformed position of the spring, or the distance between the bottom of the spring and the tabletop.