# Simple harmonic motion energy question

• Samurai44
In summary, the conversation discusses how to solve a physics problem involving kinetic and potential energy using a formula for energy in a spring. The experts suggest using the conservation of energy and the formula PE = 1/2kx^2 to solve the problem. They also mention alternative approaches using trigonometry or differential calculus. The conversation also touches on clarifying the equation given and determining the placement of variables.
Samurai44

## Homework Statement

Can I get help in part (b) of this question ?

## Homework Equations

KE=1/2 m v2
v= (2π f )√(A2 - x2)

## The Attempt at a Solution

I substituted the second equation into first one, so i got
KE= 1/2 m (2π f )2 (A2 - x2)

but then couldn't complete

You are apparently concerned with the answer to part b. One approach starts with the insight that total energy is conserved. The sum of PE + KE is a constant.

If KE is 3/4 of total energy then what fraction of total energy is PE?

The next insight is that the force required for harmonic motion is exactly the force supplied by a perfect spring. Or, simpler yet, we could simply assume that the oscillation is produced by a mass attached to a perfect spring. Do you know the formula for the potential energy of a spring?

Samurai44
jbriggs444 said:
You are apparently concerned with the answer to part b. One approach starts with the insight that total energy is conserved. The sum of PE + KE is a constant.

If KE is 3/4 of total energy then what fraction of total energy is PE?

The next insight is that the force required for harmonic motion is exactly the force supplied by a perfect spring. Or, simpler yet, we could simply assume that the oscillation is produced by a mass attached to a perfect spring. Do you know the formula for the potential energy of a spring?
Do you mean hooks law F=-kx ?

Yes. That's part of it. There is also a formula for energy in a spring as a function of displacement x. That formula can be derived by integrating F=-kx over distance. The result is PE = 1/2kx2

Samurai44
Hi,
You know that the energy is conserved right, so E is constant, why not calculating is at any point, example would be when there's no kinetic energy, Once you got E, you know that when KE = 3E/4, what is left if energy is potential energy, do this sound familier kx^2 /2 ?

Samurai44
jbriggs444 said:
Yes. That's part of it. There is also a formula for energy in a spring as a function of displacement x. That formula can be derived by integrating F=-kx over distance. The result is PE = 1/2kx2
Noctisdark said:
Hi,
You know that the energy is conserved right, so E is constant, why not calculating is at any point, example would be when there's no kinetic energy, Once you got E, you know that when KE = 3E/4, what is left if energy is potential energy, do this sound familier kx^2 /2 ?
well , iam not used to PE = 1/2kx2 :(

Kx^2/2 is the elastic potential energy of a system, where K is the spring's constant, x is the strech of the spring, and 1/2 is one half (obviously, ) and if you want a proof, W = F.x so dW = F*dx = F*x'dt = k*x*x' dt and you integrate both sided and it yields to W = 1/2kx^2 ! And now you can work with it, good luck

Samurai44
Samurai44 said:
well , iam not used to PE = 1/2kx2 :(

If you don't like using PE = 1/2 kx2 there are still a couple of other approaches to solving the original problem. Do you prefer trigonometry or differential calculus?

Samurai44
jbriggs444 said:
If you don't like using PE = 1/2 kx2 there are still a couple of other approaches to solving the original problem. Do you prefer trigonometry or differential calculus?
Isnt it possible to solve it by the equation I have given ?
it will be the same on both sides , but one will have the coefficient (3/4).
At the same time , it say in equilibrium position , so one side will have x=0, and so max. velocity (K.E)
but i am facing problem in which side to place them ( right or left ).
correct me if I am wrong please .

Samurai44 said:
Isnt it possible to solve it by the equation I have given ?
it will be the same on both sides , but one will have the coefficient (3/4).
At the same time , it say in equilibrium position , so one side will have x=0, and so max. velocity (K.E)
but i am facing problem in which side to place them ( right or left ).
correct me if I am wrong please .

The equation seems to be missing a factor of sin(theta).

Edit: I take that back. That's what the ##\sqrt{A^2-x^2}## is supposed to cover.

So if you know that the total energy E is equal to KE alone when x=0 (because this is the point where PE is presumably taken as zero), that should give you an equation.

Last edited:

## 1. What is simple harmonic motion energy?

Simple harmonic motion energy refers to the energy associated with an oscillating system, such as a mass-spring system, that follows a sinusoidal pattern. It is a type of mechanical energy that is constantly being transferred between potential and kinetic energy as the system moves back and forth.

## 2. How is the energy of a simple harmonic motion calculated?

The energy of a simple harmonic motion can be calculated using the equation E = 1/2kA^2, where E is the total energy, k is the spring constant, and A is the amplitude (maximum displacement) of the oscillating system.

## 3. What factors affect the energy of a simple harmonic motion?

The energy of a simple harmonic motion is affected by the mass of the object, the spring constant, and the amplitude of the oscillation. Other factors such as friction and air resistance may also play a role in the overall energy of the system.

## 4. Can the energy of a simple harmonic motion be changed?

Yes, the energy of a simple harmonic motion can be changed by altering the factors that affect it, such as changing the mass or spring constant of the system. Energy can also be added or removed through external forces, such as damping or external work.

## 5. What are some real-world examples of simple harmonic motion energy?

Some common examples of simple harmonic motion energy include the motion of a pendulum, the oscillation of a spring, and the vibrations of guitar strings. These systems follow a sinusoidal pattern and exhibit the transfer of energy between potential and kinetic forms.

• Introductory Physics Homework Help
Replies
51
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
617
• Introductory Physics Homework Help
Replies
11
Views
338
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
553
• Introductory Physics Homework Help
Replies
7
Views
249
• Introductory Physics Homework Help
Replies
7
Views
344
• Introductory Physics Homework Help
Replies
17
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
994
• Introductory Physics Homework Help
Replies
1
Views
1K