Finding Phase Constant for Harmonic Oscillator

In summary, the phase constant for a harmonic oscillator with velocity function v(t) and position function x(t) has a value of 4.068 rad, as the velocity maximum is 9.375 cm/s and the position maximum is 7.50 cm/s. The phase angle is determined to be in the fourth quadrant and is calculated as sin^-1(7.5/-9.375).
  • #1
GatorJ
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Homework Statement


What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in Fig. 15-30 if the position function x(t) has the form x = xmcos(ωt + φ)? The vertical axis scale is set by vs = 7.50 cm/s.
[PLAIN]http://img227.imageshack.us/img227/4729/qu1512.gif [Broken]

Homework Equations


x = xmcos(ωt + φ)
v=-ωxmsin(ωt + φ)
vm=ωxm

The Attempt at a Solution



From graph, vm=9.375 cm/s

vm=9.375 cm/s = ωxm

xm=9.375/ω

At t=0, v(0)=7.5 cm/s=-ωxmsin(φ)

φ=sin-1(7.5/-ωxm)

φ=sin-1(7.5/-ω*9.375/ω)

φ=sin-1(7.5/-9.375)= -.927 rad

I still got it wrong and not sure where I messed up. Only thing that I can think of is that I incorrectly assumed t=0 is 7.5 cm/s and if that's the case then I don't know where to begin on this problem.
 
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  • #2
Phase angle is always positive.
In this problem phase angle is in the fourth quadrant.
 
  • #3
It is correct, but try to give in positive angle with the same sine: pi-phi= 4.068 rad.

ehild
 
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What is a harmonic oscillator?

A harmonic oscillator is a system that exhibits harmonic motion, which is a type of periodic motion where the displacement of the system from its equilibrium position is directly proportional to the restoring force acting on it. Examples of harmonic oscillators include a mass attached to a spring and a pendulum.

What is the phase constant for a harmonic oscillator?

The phase constant for a harmonic oscillator is a value that determines the starting point of the oscillation. It is represented by the variable phi (φ) and is usually measured in radians. It is important in calculating the position, velocity, and acceleration of the oscillator at any given time.

How do you find the phase constant for a harmonic oscillator?

The phase constant can be found by using the initial conditions of the oscillator, such as its initial displacement and velocity, and plugging them into the equation for harmonic motion: x(t) = A*cos(ωt + φ). Solving for φ will give you the phase constant.

Why is the phase constant important in studying harmonic oscillators?

The phase constant is important because it determines the starting point of the oscillator's motion. It also affects the amplitude and frequency of the oscillation. By knowing the phase constant, we can accurately predict the behavior of the oscillator at any given time.

Can the phase constant change over time for a harmonic oscillator?

No, the phase constant remains constant for a given harmonic oscillator. It is a characteristic of the system and does not change unless there is a change in the initial conditions or the system itself is altered. However, the phase constant can vary for different harmonic oscillators with different initial conditions or parameters.

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