How Is Simple Harmonic motion possible here?

In summary, the conversation discusses how amplitude is conserved on both sides of a mass that is subjected to different forces in simple harmonic motion. The net force is determined as a function of displacement and it is shown to be the same as a mass attached to a single spring with a spring constant. The symmetrical force acting on the mass allows for the repetition of factors such as velocity. The conservation of energy is responsible for the speed being the same at the equilibrium point.
  • #1
Hydrous Caperilla
62
7
One thing I don't understand is that How Amplitude is conserved on both sides if the mass is subjected to different forces on either side of this shm...
 

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  • #2
What is the net force as a function of displacement?
 
  • #3
Dale said:
What is the net force as a function of displacement?

If I displace it towards left and then release it ,the net force will be F=(K1+K2)X towards right and then it will reach the equilibrium point and then again experience (K1+K2)X towards left which seems awfully like an even function to me
 
  • #4
So this is the exact same force as for a mass attached to a single spring with a spring constant k=K1+K2
 
  • #5
Dale said:
So this is the exact same force as for a mass attached to a single spring with a spring constant k=K1+K2

Kay Makes Sense to Me somewhat...Is that the reason that velocity is also repeated.ie the mean velocity is same after oscillating from mean to left and then coming to mean once again...Can you tell me more about this symmetrical force acting which makes such factors repeat
 
  • #6
Your period key may need to be removed and cleaned. It appears to be sticking.

The fact that the speed is the same at the equilibrium point is a consequence of the conservation of energy, not the symmetry of the force.
 
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Likes sophiecentaur and Hydrous Caperilla
  • #7
Kay makes sense to me now.The conservation of enrgy is responsible for that consequence.Thanx for the reply
 

1) What is simple harmonic motion and how is it possible?

Simple harmonic motion is a type of periodic motion where an object moves back and forth in a regular pattern. It is possible because of the restoring force acting on the object, which is proportional to the displacement from the equilibrium position. This causes the object to oscillate around the equilibrium position.

2) How does the motion of a pendulum demonstrate simple harmonic motion?

A pendulum consists of a mass attached to a string or rod that is free to swing back and forth. When the pendulum is displaced from its equilibrium position, the restoring force (gravity) causes it to oscillate, demonstrating simple harmonic motion. The period of a pendulum is directly proportional to the length of the string and inversely proportional to the acceleration due to gravity.

3) Can simple harmonic motion occur in other systems besides a pendulum?

Yes, simple harmonic motion can occur in other systems such as a mass-spring system or a vibrating guitar string. In these systems, the restoring force is provided by the spring or tension in the string, respectively.

4) What is the relationship between simple harmonic motion and equilibrium?

In simple harmonic motion, the equilibrium position is where the object is at rest and the restoring force is zero. When the object is displaced from equilibrium, the restoring force increases, causing the object to oscillate back and forth around the equilibrium position.

5) How is simple harmonic motion used in real-world applications?

Simple harmonic motion has many practical applications, such as in clocks, musical instruments, and shock absorbers. It is also used in engineering and physics to model and analyze systems that exhibit periodic motion.

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