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mrblanco said:Homework Statement
Find the natural frequency
Homework Equations
On picture
The Attempt at a Solution
Just need help with the equation of motion.
mrblanco said:This is all the information I was given. The block is moving to the left but no values are given. The middle lever has a pin connection
mrblanco said:Also, I know I have to use rF1+/-rF2=I(alpha) just not sure how
mrblanco said:I'm thinking that has to be part of the equation of motion for the block
mrblanco said:If I only considered the spring on the right, I get a complex answer...View attachment 88790
mrblanco said:
mrblanco said:
mrblanco said:If i move the block to the right that would also compress the k2 spring. Aren't the springs working against each other because of the lever? When one pulls in one direction, the other pulls in the opposite direction.
I know I'm missing something here but I can't seem to figure it out
mrblanco said:Springs in series so 1/k +1/k2
Natural frequency is the frequency at which a system will oscillate when disturbed from its equilibrium position. It is important because it determines the behavior and stability of the system.
The equation of motion for natural frequency can be found by using Newton's Second Law of Motion (F=ma) and Hooke's Law (F=-kx) for a spring-mass system. The resulting equation is a second-order differential equation that can be solved to find the natural frequency.
The natural frequency of a system is affected by the mass of the object, the stiffness of the spring, and the damping coefficient. Increasing any of these factors will result in a higher natural frequency, while decreasing them will result in a lower natural frequency.
Resonance occurs when a system is driven at its natural frequency, resulting in larger oscillations. This can be seen in everyday objects such as a swinging pendulum or a tuning fork. Natural frequency and resonance are closely related as they both involve the behavior of a system at its natural frequency.
Yes, the natural frequency of a system can be changed by altering the mass, stiffness, or damping of the system. This can be done by adding or removing weight, changing the material of the spring, or adding a damping mechanism. By changing these factors, the natural frequency of the system can be adjusted to meet specific requirements.