# Simple harmonic motion waves

1. Oct 11, 2012

### Shan K

I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question is , is there any derivation which can show that the constant is the frequency of the shm .

2. Oct 11, 2012

### Studiot

It would help if you told us what the system was.
Spring and mass vertical or horizontal?
Pendulum?
?

The basis of SHM is always that the restoring force is proportional to the displacement (from the mean position). Since the force tends to return the system to the mean position is acts in the opposite direction to the displacement so one is negative.

3. Oct 11, 2012

### Shan K

It was for pendulum

4. Oct 11, 2012

### bgq

I am not sure what your question is; anyway, the equations of shm could be derived by applying the principle of conservation of mechanical energy.

5. Oct 11, 2012

### Shan K

Let me show u the derivation .
We know that for shm

force varies as negetive displacement

therefore,
force equal to some constant times negetive displacement

they said that this constant is equal to the frequency of the shm . I want to know how ?
( sorry for writing all the equation in words cus my mobile doesn't support to write equations with some special charecters . )

6. Oct 11, 2012

### Studiot

Sorry to ask another question but I don't want to post something different from your course.

What definition of SHM are you using?

7. Oct 11, 2012

### AlephZero

No, because the units mean that can't possibly be correct.

But for a system with unit mass, the constant is equal to the frequency squared (frequency measured in radians/second, not Hz).

This should be explained in any textbook or website about the dynamics of single degree of freedom (SDOF) systems.

For a pendulum, the "unit mass" part doesn't matter, since the force (i.e. weight) is proportional to the mass.

8. Oct 11, 2012

### Shan K

i don't have studied any kind of definition on shm . What i have studied is some properties of that like it has a restoring force