# Help with this problem about a mass oscillating on a spring

• wobblegobble
In summary, a mass (M) attached to a spring (K) moves in a one dimensional plane (horizontally). The displacement is denoted by x and the force of the spring on the mass is given by F = -kx, where k is the spring constant.1) The minimum work required to bring the mass from x=0 to x=x0 is equal to the change in potential energy (PE), which is given by PE = 1/2kx0^2.2) When the mass is released from x=x0, the potential energy is converted to kinetic energy (KE). At x=x0/2, all the potential energy has been converted to kinetic energy, and the mass will have a
wobblegobble
Homework Statement
hooke's
Relevant Equations
displacement = x
force of spring -> mass (M) = F = -kx
A mass (M) is attached to a spring (K). Mass moves in a one dimensional plane (horizontally)
1) If mass M is initially at x=0, what is the minimum Work required to bring it to x=x0 ? PE ?
2) M is released from x=x0, PE when x=xo/2 ? KE ?
3) PE when x=0 ? KE ?
4) PE when x=-x0/2 ? KE ?
5) What is the largest negative x value will become ? PE ? KE ?

velocity is not nessesary to find for 2,3,4

Last edited by a moderator:
Welcome to the PF.

wobblegobble said:
Homework Statement:: hooke's
Relevant Equations:: displacement = x
force of spring -> mass (M) = F = -kx

A mass (M) is attached to a spring (K). Mass moves in a one dimensional plane (horizontally)
1) If mass M is initially at x=0, what is the minimum Work required to bring it to x=x0 ? PE ?
2) M is released from x=x0, PE when x=xo/2 ? KE ?
3) PE when x=0 ? KE ?
4) PE when x=-x0/2 ? KE ?
5) What is the largest negative x value will become ? PE ? KE ?

velocity is not nessesary to find for 2,3,4
We require that you show your best efforts to work on this problem before we can provide tutorial help.

Please post the rest of the Relevant Equations, and start to use them to answer these questions. Thank you.

## 1. What is the equation for the motion of a mass oscillating on a spring?

The equation for the motion of a mass oscillating on a spring is x = A cos(ωt + φ), where x represents the displacement of the mass, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase constant.

## 2. How does the mass affect the period of oscillation?

The mass has no effect on the period of oscillation. The period is solely determined by the spring constant k and the mass does not appear in the equation for period, T = 2π√(m/k).

## 3. What is the relationship between the spring constant and the frequency of oscillation?

The frequency of oscillation is directly proportional to the square root of the spring constant. This means that as the spring constant increases, the frequency of oscillation also increases.

## 4. How does the amplitude of oscillation affect the energy of the system?

The amplitude of oscillation has a direct relationship with the energy of the system. As the amplitude increases, the energy also increases. This is because the potential energy stored in the spring increases as the amplitude increases.

## 5. Can the motion of a mass on a spring be considered simple harmonic motion?

Yes, the motion of a mass on a spring can be considered simple harmonic motion as long as the restoring force is directly proportional to the displacement from equilibrium and the motion is periodic. This is true for most real-world systems as long as the amplitude of oscillation is small.

• Introductory Physics Homework Help
Replies
24
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
560
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
311
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
6
Views
276
• Introductory Physics Homework Help
Replies
10
Views
1K