Finding the Phase Constant in a Mass/Spring System

In summary, to find the phase constant for a mass/spring system with given information of spring constant, mass, position, and velocity, the first step is to solve for the angular frequency (ω) using the equation ω = √(k / m). Then, using the equations x(t) = xmcos(ωt + Φ) and v(t) = -ωxmsin(ωt + Φ) at t = 0, you can eliminate the amplitude (xm) to find the phase constant (Φ).
  • #1
emilli
1
0

Homework Statement


A mass/spring system is set in motion. Find the phase constant with the given information.

Given:
k = 8 N/m (spring constant)
m = 0.1 kg (mass attached to string)
x0 = -0.12 m (position at t = 0)
v0 = 0.9 (velocity at t = 0)

Homework Equations


x(t) = xmcos(ωt + Φ)
v(t) = -ωxmsin(ωt + Φ)
k = mω2

The Attempt at a Solution


I first solved for ω using the given spring constant and mass: ω = √(k / m) = √(8N/m / 0.1kg) = 8.94 rad/s
At t = 0,
x(0) = xmcos(Φ)
v(0) = -ωxmsin(Φ)
Unfortunately, this was where I became stumped. I don't know how to find the amplitude(xm) which is the only thing I needed to solve for the phase constant. Any hints to what I should do?
 
Physics news on Phys.org
  • #2
It looks like you may have 2 equations and 2 unknowns.

Edit: Welcome to Physics Forums.
 
  • #3
emilli said:
how to find the amplitude(xm)
You don't need to find it, you need to eliminate it.
 
  • Like
Likes TomHart

1. What is the phase constant?

The phase constant is a term used in physics and engineering to describe the starting point of a wave or oscillation. It represents the initial position of the wave or oscillation, and is usually measured in degrees or radians.

2. How is the phase constant calculated?

The phase constant can be calculated using the formula Φ = tan-1(y/x), where y is the vertical displacement of the wave and x is the horizontal displacement. Alternatively, it can also be calculated using the formula Φ = 2π/λ * Δx, where λ is the wavelength of the wave and Δx is the horizontal displacement.

3. What is the significance of the phase constant?

The phase constant is important because it helps us understand the behavior and characteristics of waves and oscillations. It is used to determine the amplitude, frequency, and wavelength of a wave, and can also be used to predict the future behavior of the wave.

4. How does the phase constant affect the shape of a wave?

The phase constant determines the starting point of a wave, which in turn affects the overall shape of the wave. A change in the phase constant can result in a shift in the wave's starting point, causing a change in the wave's amplitude, frequency, and wavelength.

5. Can the phase constant be negative?

Yes, the phase constant can be negative. This means that the wave or oscillation is starting at a point that is shifted backwards from the origin. It is also possible for the phase constant to be greater than 360 degrees or 2π radians, as it represents a full rotation or cycle of the wave.

Similar threads

Energy stored in a double spring system
    • Introductory Physics Homework Help
Replies
17
Views
318
Why can we move the spring with constant speed when we apply a force?
    • Introductory Physics Homework Help
Replies
29
Views
930
Position and acceleration in simple harmonic motion given velocity
    • Introductory Physics Homework Help
Replies
16
Views
411
Simple Harmonic Oscillator: Mass Spring System
    • Introductory Physics Homework Help
Replies
2
Views
2K
Stretching of a rotating spring
    • Introductory Physics Homework Help
Replies
8
Views
343
Consistency of Faraday's Law and Electric Field Equation in Optics
    • Introductory Physics Homework Help
Replies
2
Views
712
Solving for the Damping Constant
    • Introductory Physics Homework Help
Replies
11
Views
2K
Two masses on a rotating platform
    • Introductory Physics Homework Help
Replies
3
Views
874
Find spring constant k using an electrical circuit
    • Introductory Physics Homework Help
Replies
10
Views
922
How Is Potential Energy Converted to Kinetic Energy in Physical Systems?
    • Introductory Physics Homework Help
Replies
6
Views
322

Hot Threads

Recent Insights

Back
Top