Differential Eq. for Spring-Mass System on Seesaw: Case 1 & 2

In summary, the conversation discusses a seesaw that is balanced with a fulcrum point and has a spring attached at one end. The seesaw has a total mass attached to the spring, creating a spring-mass system. The question arises about the oscillation of the seesaw around the pivotal point and the differential equation of the system. In a similar scenario, with both ends of the seesaw attached to springs, the conversation also addresses the relevant equations and attempts to solve the problem. A hint is given to consider the seesaw with the mass-spring system as a superposition of simple harmonic motion. However, clarification is needed on the visual of the seesaw-spring system in order to provide further assistance.
  • #1
Tahir Mushtaq
2
0
case 1: Seesaw is balanced with its fulcrum point or pivotal point. At one end of seesaw, the spring (with spring constant K1) is attached. Now the seesaw has total mass M which is attached to spring, form a spring-mass system. I confuse on this point that the oscillation of seesaw will be around pivotal point. Then what is differential equation of spring-mass system.

case 2: The same case with both ends of Seesaw is attached with springs having spring constant K1 and K2. Then what is differential equation of this system.
 
Physics news on Phys.org
  • #2
1) What equations would be relevant to this problem?

2) What have you tried to do to solve it so far?

3) Hint: Can you derive an Equation of Motion for a simple mass-spring system (without a seesaw)? If so, can you consider the motion of the seesaw with the mass-spring system as a superposition of simple harmonic motion?

I cannot visualize your seesaw-spring system. If you can describe it better (or link to a picture), maybe I can help more.
 

1. What is a spring-mass system on a seesaw?

A spring-mass system on a seesaw is a physical system that consists of a mass attached to a spring, which is in turn attached to a seesaw. The seesaw is a lever that pivots on a fulcrum, allowing the mass to move up and down as the spring is compressed or stretched.

2. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. In the context of a spring-mass system on a seesaw, it is used to model the motion of the mass as it oscillates.

3. What is Case 1 for the spring-mass system on a seesaw?

Case 1 refers to the scenario where the mass is initially at rest at the equilibrium position of the seesaw. This means that the seesaw is balanced, and the spring is neither compressed nor stretched. The differential equation for this case describes the simple harmonic motion of the mass as it moves up and down.

4. What is Case 2 for the spring-mass system on a seesaw?

Case 2 refers to the scenario where the mass is initially displaced from the equilibrium position and released. This causes the seesaw to become unbalanced, and the spring to either be compressed or stretched. The differential equation for this case describes the damped harmonic motion of the mass as it moves towards the equilibrium position.

5. What factors affect the motion of the spring-mass system on a seesaw?

The motion of the spring-mass system on a seesaw is affected by various factors such as the mass of the object, the stiffness of the spring, and the damping coefficient. These factors determine the amplitude, frequency, and decay of the oscillations of the mass. Other external factors, such as the force of gravity and friction, can also affect the motion of the system.

Similar threads

Spring-mass system with a pendulum using Lagrangian dynamics
    • Advanced Physics Homework Help
Replies
15
Views
2K
Eigenvalues and vectors of a 4 by 4 matrix
    • Advanced Physics Homework Help
Replies
3
Views
2K
Question about Lagrangian density
    • Advanced Physics Homework Help
Replies
1
Views
1K
2 degree of freedom system modeling
    • Advanced Physics Homework Help
Replies
3
Views
1K
Lagrangian of a mass bewteen two springs with a pendulum hanging down
    • Advanced Physics Homework Help
Replies
9
Views
3K
Help with coefficients matrix in spring system
    • Advanced Physics Homework Help
Replies
5
Views
1K
I Two-Mass Oscillator: Plotting Amplitudes Over Frequencies in Hertz
    • Mechanics
Replies
5
Views
361
Stretching of a rotating spring
    • Introductory Physics Homework Help
Replies
8
Views
336
Balancing a Seesaw: Finding Mass with Torque
    • Introductory Physics Homework Help
Replies
7
Views
8K
I Spring balance analysis from a system point of view
    • Classical Physics
Replies
24
Views
723

Hot Threads

Recent Insights

Back
Top