# Amplitude of the spring motion

• Vengeance
In summary, the conversation discusses solving for the force constant and amplitude of a spring attached to a mass undergoing simple harmonic motion, as well as finding the maximum speed of a mass attached to a horizontal spring after a given time period. The solution involves understanding the equations for kinetic and potential energies and their relationship to the total energy of the system, as well as considering the initial displacement of the spring. Further clarification may be needed to fully solve the problems.
Vengeance
A 0.38 kg mass is attached to a spring and executes simple harmonic motion with a period
of 0.08 s. The total energy of the system is 1.9 J. Find:

a) the force constant of the spring. Answer in units of N/m.
b) the amplitude of the motion. Answer in units of m.

For a, I got 2341.655 N/m by using the formula k= (T^2/4pi^2m)

but how do I solve for b?

And here is another question:

A 1.02 kg mass is attached to a horizontal spring. The spring is initially stretched by 0.0478 m and the mass is released from rest there. After 0.507 s, the speed of the mass is zero (for the first time after being released). What is the maximum speed of the mass? Answer in units of m/s.

I'm so lost in this questions because it is really confusing.

Vengeance said:
but how do I solve for b?

Assuming that there is no friction, the total energy is constant. Do you have any equations, or can you form one, that relates the total energy (the only given datum that you have yet to use) to the amplitude?

Nope, that's what I've been looking for till now. I'm doing a research on HOW to relate those equations...What about my other problems? and btw, this is an AP Physics course

Vengeance said:
Nope, that's what I've been looking for till now. I'm doing a research on HOW to relate those equations

I guess you are supposed to derive the equation then? It's such a simple equation, but the derivation may take you some time.

Hint: What are the equations for K(t) and U(t), where K(t) and U(t) are the kinetic and potential energies of the system for some time t? How are these quantities related to the total energy?

are there any other people want to help me here?

Vengeance said:
And here is another question:

A 1.02 kg mass is attached to a horizontal spring. The spring is initially stretched by 0.0478 m and the mass is released from rest there. After 0.507 s, the speed of the mass is zero (for the first time after being released). What is the maximum speed of the mass? Answer in units of m/s.

I'm so lost in this questions because it is really confusing.

At what point of the oscillation would the speed of the mass equal zero? What term in regard to distance does this correspond to? How is this distance related to the initial displacement that is given?

You asked for help, but I have only asked you more questions. =) The problem should become clearer when you answer these questions.

Vengeance said:
are there any other people want to help me here?

You don't like my help? Perhaps, you haven't thought about the problem enough. Physics isn't automatic.

I'll shall refrain from further assistance. Btw, welcome to the Physicsforums.

okay okay...anyways, I got the answer for B in the first questions. But I still can't figure out the answer for the second one...my friend told me to put it into the equation:
1/2 K x^2 = 1/2 mv^2

and solve for v but I didn't get the answer right...any suggestions??

## 1. What is the amplitude of a spring motion?

The amplitude of a spring motion is the maximum displacement or distance from equilibrium that the spring undergoes during its oscillations.

## 2. How is the amplitude of a spring motion calculated?

The amplitude can be calculated by measuring the distance between the equilibrium point and the maximum displacement of the spring. It can also be calculated using the formula A = (xmax - xeq), where xmax is the maximum displacement and xeq is the equilibrium point.

## 3. What factors affect the amplitude of a spring motion?

The amplitude of a spring motion can be affected by the mass of the object attached to the spring, the stiffness of the spring, and the initial displacement of the spring.

## 4. What is the relationship between amplitude and frequency in spring motion?

The amplitude and frequency in spring motion have an inverse relationship. This means that as the amplitude increases, the frequency decreases, and vice versa. This relationship is described by the equation ω = √(k/m), where ω is the angular frequency, k is the spring constant, and m is the mass attached to the spring.

## 5. How does the amplitude of a spring motion change over time?

The amplitude of a spring motion will decrease over time due to the damping effect, which reduces the energy and amplitude of the oscillations. However, if the spring is undamped, the amplitude will remain constant over time.

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