# Simple Harmonic Motion Question

• zstraught
In summary, the individual first uses Young's modulus to calculate the change in position (delta y) and then uses the equation T = 2delta y sqrt(m/k) to determine the frequency (f) of oscillations around the equilibrium position. However, after substituting values and solving for f, they get a significantly incorrect result.
zstraught
Homework Statement
A copper rod (length=2.0 m, radius=3.0×10−3 m) hangs down from the ceiling. A 9.0-kg object is attached to the lower end of the rod. The rod acts as a “spring,” and the object oscillates vertically with a small amplitude. Ignoring the rod's mass, find the frequency f of the simple harmonic motion.
Relevant Equations
F=-kx
w = sqrt(k/m)
T = 2pi x r sqrt(m/k)
First I use young's modulus to solve for delta y. I get 5.67x10 -5.
I am not sure what to do after this, but this is my attempt.

Next I do T = 2delta y sqrt(m/k) (I am not sure if I am supposed to put 2 delta y)

Solving for f, i get f = 1/(2delta y sqrt(m/k))

F = kx, mg = kx, m = kx/g

Substituting in the equation above, I get f = 1/(2deltay sqrt(x/g))

Plugging in the numbers, I get a very large number around 3 million, which is totally wrong.

zstraught said:
First I use young's modulus to solve for delta y. I get 5.67x10 -5.
That just gives you the equilibrium position. Consider oscillations around there.

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, with a constant amplitude and a constant period. It is caused by a restoring force that is directly proportional to the displacement of the object from its equilibrium position.

## 2. What are some examples of simple harmonic motion?

Some examples of simple harmonic motion include a pendulum, a mass on a spring, and a swinging door. These all exhibit back-and-forth motion around an equilibrium point due to a restoring force.

## 3. How is simple harmonic motion related to the concept of frequency?

Simple harmonic motion is directly related to frequency, as the frequency of an object's motion is determined by its period (the time it takes to complete one full cycle). The higher the frequency, the shorter the period and the faster the object oscillates.

## 4. What is the formula for calculating the period of simple harmonic motion?

The formula for calculating the period of simple harmonic motion is T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant of the restoring force.

## 5. What factors can affect the amplitude of simple harmonic motion?

The amplitude of simple harmonic motion can be affected by the initial displacement of the object, the strength of the restoring force, and any external forces acting on the object. Additionally, the amplitude may decrease over time due to energy loss through friction.

### Similar threads

• Introductory Physics Homework Help
Replies
16
Views
608
• Introductory Physics Homework Help
Replies
7
Views
247
• Introductory Physics Homework Help
Replies
11
Views
334
• Introductory Physics Homework Help
Replies
51
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
231
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
991
• Introductory Physics Homework Help
Replies
2
Views
1K