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Seçkin Kum 2019719114 10/02/2021

Spring Mass System

 
You are seeing on the left a horizontal spring mass system.
When you pull the mass a little bit forward along the +x axis and pulled off, you broke the equilibrium condition.
 
  • Displacement on the spring creates force which direction is initial position od the system.
  • Then system starts to move. As you see mass is going right then starts to move left again. Without any friction in the system, this movement goes continuously.
 
The main thing here is spring force, it is directly related with type of the spring and how much displacement spring have.
 
If displacement is occurring at the positive direction spring starts to apply force through the negative direction.
        

F=kx

If we add friction to the system, eventually system will be stopped.
 
Because friction always has a force backwards to the motion.
 
Friction is mainly related with mass of the moving box and friction coefficient of surface.
  • If surface has more grained structure than more friction occurs.
  • If your box is heavy than you have more friction.
  • It is independent from the system velocity. Friction force is applying always steady except from mass change during the movement.
 
        Fr=umgFriction Force = Friction Coefficient * Weight

The left you are seeing that vertical simple harmonic motion.

 
Mass is moving up and down. As you see when the mass goes down the
 
maximum displacement position, its velocity decreases to zero the same
 
thing happening when the mass move maximum upward position.
 
The mass has the maximum velocity when its passing from the zero deflection point.
Time Speed Time Displacement
Displacement and velocity has opposite relation ship. When displacement is maximum or minimum, the velocity become zero.
 
Same for the velocity, when velocity is maximum displacement is zero.
 
As you seen from the graph the movement is steady, velocity and displacement graphs look like sinus waves.
 
  • If we apply differentiation on displacement graph, we can achieve the velocity.
  • If we apply differentiation on velocity graph, we can get acceleration.
Frquency= 1/T Frquency=0.1Hz T=10s Frquency=0.5Hz T=2s Period= 10s Period= 2s
You can find some critical formulation in this section.
Frequency means how many times the movement completed its cycle in one second.
T means period, one period equals to completion of movement.
You can calculate over the graph. Select highest point and count when the graph comes again it highest point again.
  • The amount of time pass from the highest to highest point is period.
  • You can calculate frequency by 1 / T.

THANK YOU!

 

Seçkin Kum -2019719114

10/02/2021