What Is the Phase Constant in Simple Harmonic Motion?

In summary: OR arccos(0.2)= 78.48 degrees. It is possible that your book has the phase angle in degrees rather than radians?
  • #1
edge
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The bow of a 5.0E6 kg destroyer undergoes a simple vertical harmonic motion with a period of 8.0 s and amplitude of 2.0 m. The motion of the boat is recorded by a sailor. At t = 0 s, the boat is at 40 cm above the equilibrium point with an initial velocity of -25 cm/s.

a) Find the phase constant, the angular frequency, and write the equations of motion, velocity, and acceleration.

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Sadly enough, I'm having trouble finding the phase constant. I'm not sure exactly what I'm doing wrong...but due to circumstances I don't have the correct answer to look at, only one incorrect one. There are more parts to this problem but I haven't tried them yet, since I'm stuck here... So I may edit this post with another question when I can figure this one out.

I'm using x = A cos (wt + phi) , .4 = 2 cos [(-.25)(0) + phi] which gives me 1.37, the incorrect answer.

***/Edit***
d) A 90-kg sailor is standing on a scale in a bankroom near the bow. What are the maximum and minimum readings on the scale in Newtons?
- For this one would I just use a(max) = (omega^2)*A and add that to 9.81 to get the acceleration. Then multiply that by his mass? For the minimum I would just subract a(max) from gravity and do the same?

e) The ship main computer is mounted on a suspension system to protect it against vibrations and shocks. Protected by this system, a 20 Hz oscillation loses half its energy in .5 s. What are the fractional energy loss per cycle and the Q factor of the suspension system? - Absolutely no clue on this one.
***/Edit Off***


Thank you for your time and any help is greatly appreciated!

-Edge
 
Last edited:
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  • #2
.4 = 2 cos [(-.25)(0) + phi] so cos[phi]= 0.2 and therefore
phi= arccos(0.2)= 1.37 radians OR arccos(0.2)= 78.48 degrees. Is it possible that your book has the phase angle in degrees rather than radians?
 
  • #3
Well the GTA for my class is who said that answer was wrong so maybe he just misread it? I'm not really sure of any other way to find the phase constant. Oh well, I really do appreciate the help! I'm just about to update my post with another part of the problem, if you'd like to try to help on that one too.

-Edge
 

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where an object oscillates back and forth around an equilibrium point due to a restoring force that is directly proportional to the displacement from the equilibrium point. It follows a sinusoidal pattern and has a constant period and amplitude.

2. What causes Simple Harmonic Motion?

Simple Harmonic Motion is caused by a restoring force, which is a force that brings an object back to its equilibrium position. In SHM, the restoring force is directly proportional to the displacement from the equilibrium point, according to Hooke's Law.

3. What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x = A sin(ωt + φ), where x is the displacement from the equilibrium point, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation represents the sinusoidal motion of an object undergoing SHM.

4. What are some real-life examples of Simple Harmonic Motion?

Some examples of Simple Harmonic Motion in everyday life include the swinging of a pendulum, the motion of a mass on a spring, and the vibrations of guitar strings. SHM can also be observed in the oscillations of a car's suspension system and in the motion of a diving board.

5. How is Simple Harmonic Motion related to energy?

Simple Harmonic Motion involves the exchange of potential and kinetic energy. At the equilibrium point, all of the energy is in the form of potential energy. As the object moves away from the equilibrium point, the potential energy decreases and the kinetic energy increases. At the maximum displacement, all of the energy is in the form of kinetic energy. As the object moves back towards the equilibrium point, the process repeats itself. This energy exchange is what allows the object to continue oscillating back and forth in SHM.

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