How Does the Phase Angle in SHM Equations Affect Displacement and Energy?

In summary, the first question asks whether phi would be different for the function x = A sin (wt + phi) and x = A cos (wt + phi). The answer is that phi would be equal to pi instead of 0, as it would be for x = A cos (wt + phi). The second question asks whether elastic potential energy can equal kinetic energy for a mass attached to a spring undergoing simple harmonic motion. The answer is no, they will never be equal at any point x.
  • #1
sapiental
118
0
question 1)

If a simple harmonic oscillation is described by the function

x = A sin (wt + phi)

would phi be the opposite of what it would be for a SHM described by the function

x = A cos (wt + phi)

I.e if the graph for for x = A sin (wt + phi) , when t = 0, x = +A. would phi be equal to pi instead of 0( as it would for x = A cos (wt + phi)question 2)

For a mass m attached to a spring that undergoes simple harmonic motion, The spring
constant is k.

Does the elastic potential energy ever equal the kinetic energy at one point x?

this isn't a homework question, just my curiosity..

Thanks
 
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  • #2
1. If [tex] x = A\sin(\omega t + \phi) [/tex] and [tex] x = +A [/tex] at [tex] t = 0 [/tex], then [tex] A = A\sin(\phi) [/tex].

So [tex] \phi = \frac{\pi}{2} [/tex]
 
  • #3
thanks alot!
 

Related to How Does the Phase Angle in SHM Equations Affect Displacement and Energy?

1. What is phase angle in simple harmonic motion?

The phase angle in simple harmonic motion (SHM) is a measure of the position of an object in its oscillatory motion. It is the angle between the object's current position and its equilibrium position, and it determines the direction and magnitude of displacement at any given time.

2. How is phase angle related to frequency and period in SHM?

The phase angle is directly related to the frequency and period of SHM. As the frequency increases, the period decreases, causing the phase angle to increase. This means that the object completes more oscillations in the same amount of time, resulting in a larger phase angle.

3. Can the phase angle be negative in SHM?

Yes, the phase angle can be negative in SHM. This occurs when the object starts its oscillatory motion at a point that is behind the equilibrium position, resulting in a negative angle. The negative phase angle indicates that the object is moving in the opposite direction of the positive phase angle.

4. How does the phase angle affect the amplitude of SHM?

The phase angle does not directly affect the amplitude of SHM. However, a larger phase angle indicates that the object is further away from the equilibrium position, resulting in a greater amplitude. Additionally, the amplitude can be calculated from the phase angle using the equation A = x/tan(ϕ), where A is the amplitude, x is the displacement, and ϕ is the phase angle.

5. What factors can affect the phase angle in SHM?

The phase angle in SHM can be affected by various factors such as the initial conditions of the system, the mass of the object, the spring constant, and any external forces acting on the object. Additionally, changes in the frequency or amplitude can also impact the phase angle.

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