Simple Harmonic Motion

In summary, the conversation discusses finding the phase angle in a simple harmonic motion example. They use the formula v(t)=-vmaxsin(\omegat + \varphi) and solve for \varphi using vmax and v(0). However, they mention adding 2k*pi to the angle as it produces the same result. They also clarify that using (pi-x_rad) as the angle is not the phase angle as it represents the particle moving towards the equilibrium point instead of away from it. The correct answer for the phase angle is at omega+2n*pi, where n is any integer. This is because all particles in the same phase along the wave have the same velocity, direction, and distance from the mean
  • #1
salman213
302
1
In simple harmonic motion example there is a question

velocity max is given
velocity at time = 0 is given (which is not equal to maximum velocity --> not at equilibrium point at time=0)
graph is also given of the velocity function

IT asks to find the phase angle

in the solution they use the formula

v(t)=-vmaxsin([tex]\omega[/tex]t + [tex]\varphi[/tex])

using vmax and v(0) they solve for [tex]\varphi[/tex]

then they add 2pie to it and say the answer is either x rad or 2pie + xrad (where x is the answer they found)

why do they add this 2pie (i know it has the same value but it can then be k2pie where k is any integer since x rad + 2pie or x rad + 4 pie or x rad + 6pie etc. will also give u the same answer)


any help?
 
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  • #2
This is a HW question. Anyway, you've given some thought to it. You are right -- adding 2k*pi to any angle makes it the same.

Are you sure they are not saying (pi-x_rad)?
 
  • #3
no that is also an answer yes but they say it is not the phase angle because if u use the angle u get from pie - x_rad that gives u the angle when the "slope" of the graph is increasing and therefore meaning the direction of the particle moving changes. IT is suppose to be going away from the equilibirum but if u say the phase angle is pie minus xrad then that means its is going towards the equilibrium point.
 
  • #4
Then it is the simple and correct answer that at phase omega+2n*pi, the particle is in the identical state. You cannot distinguish the state of the particle between any of these states, and that is why it's called to be in the same phase. (Actually, it had been my mistake not to explain to you sooner.)

Suppose a wave is moving. Then all the particles which are in the same phase along the wave are those that that have the angles as 2n*pi + omega, where n is any integer, +ve, -ve or zero. They have the same velocity in the same direction, and are at the same distance from the mean position
 
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What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. The motion is characterized by a constant amplitude and a sinusoidal pattern.

What factors affect the period of Simple Harmonic Motion?

The period of SHM is affected by two factors: the mass of the object and the stiffness of the spring. A heavier object or a stiffer spring will result in a longer period of oscillation.

What is the relationship between Simple Harmonic Motion and Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the object from its equilibrium position. This relationship is what causes the object to experience SHM.

Can Simple Harmonic Motion be applied to real-life situations?

Yes, Simple Harmonic Motion can be observed in many real-life situations, such as the motion of a pendulum, the vibration of a guitar string, and the motion of a car's suspension system.

How does damping affect Simple Harmonic Motion?

Damping, or the reduction of amplitude over time, can affect the motion of an object in SHM by decreasing the amplitude and increasing the period of oscillation. This can be caused by external forces, such as friction, air resistance, or internal resistance within a spring.

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