Simple harmonic motion of a spring mass

In summary: As for your earlier confusion, I think you may have been confusing the amplitude of oscillation (0.02m) with the extension of the spring (0.1m). The amplitude is the maximum displacement from equilibrium, so in this case it would be 0.02m. In summary, the amplitude of the simple harmonic motion is 0.02m. The equation for a particle Q, which is x length away from particle P in a progressive wave, is y = asin(ω(t - t')), where t' is the time it takes for the wave to travel from P to Q. The minus sign in the equation is due to the shorter time of oscillation for particle Q compared to P.
  • #1
Kurokari
36
0

Homework Statement



A spring of negligible mass have an original length of 1m. A load of 2kg is later added to it, resulting in an extension of 0.1m. Then it is pulled 0.02m and released.

What is the amplitude of the simple harmonic motion.

erm basically I just want to know which is the amplitude, 0.1m or 0.02m. Based on what I am told, the amplitude is 0.02m, but I just don't get it. It would be nice if someone can explain it =)

Homework Equations


x = x0 sin(ωt)

The Attempt at a Solution



-

==================================================

The next question isn't really a homework question but an attempt on understanding the formula for a progressive wave.

Direction of wave is in the Ox-positive direction

For a particle, P, which is vibrating in a progressive wave with equation
y = asin(ωt) when t = 0, x = 0

The equation for Q particle, which is x length away from particle P with equation
y = asin(ωt - [(2∏x)/λ] ).

Question: Why does it minus the phase difference? Because to my understanding, if you want the equation of particle Q, you would add the phase different?

Again, your explanation and patience with me is greatly appreciated =)
 
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  • #2
The amplitude is the extension beyond the equilibrium point. Hence it is 0.02m.
 
  • #3
Kurokari said:
Direction of wave is in the Ox-positive direction
The equation for Q particle, which is x length away from particle P with equation
y = asin(ωt - [(2∏x)/λ] ).

Question: Why does it minus the phase difference? Because to my understanding, if you want the equation of particle Q, you would add the phase different?

Your equation for Q is for a particle 'x length away from particle P' and ON THE POSITIVE X SIDE OF of P.

Since the wave is traveling in the Ox-positive direction and Q is assumed to be further on the positve x-dir, then the time of oscillation for Q is less than that for P.

Hence the shm for Q is given by the same as that for P but for a shorter time (t - t') where t' is the time the wave takes to travel from P to Q i.e. to travel 'length x'.

This gives the shm for Q to be

y = asin[ω(t - t')].

One or two further steps one gets the equation given for Q.
 

1. What is simple harmonic motion?

Simple harmonic motion refers to the back and forth movement of an object in a straight line, where the restoring force is directly proportional to the displacement from the equilibrium position. It is a type of periodic motion that can be seen in many systems, including a spring mass system.

2. What is a spring mass system?

A spring mass system is a physical system consisting of a mass attached to a spring. When the mass is displaced from its equilibrium position, the spring exerts a restoring force, causing the mass to oscillate back and forth.

3. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*cos(ωt + φ), where x represents the position of the object, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

4. How does the mass affect simple harmonic motion?

The mass affects simple harmonic motion by changing the period and frequency of the oscillations. A larger mass will have a longer period and lower frequency, while a smaller mass will have a shorter period and higher frequency.

5. Can simple harmonic motion be applied to real-life situations?

Yes, simple harmonic motion can be seen in various real-life situations, such as the swinging of a pendulum, the vibrations of a guitar string, and the motion of a car's suspension system. It is a fundamental concept in physics and has many practical applications.

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