DR1 said:i am trying to work this out from a very confusing book what would the effect on angular frequency be by
increasing mass
increasing amplitude of vibration
increasing spring stiffness
increasing phase lag
need to get this in my head before attemping to work out questions
Consider that for the spring mass oscillator [tex]\omega=\sqrt{\frac{k}{m}}[/tex].This tells you that the only factors that affect the natural angular frequency is determined by the physical properties of the system.So increasing the mass actually lowers the angular frequency.This is because a more massive object is harder to accelerate(second law).DR1 said:an increased mass would lead to an increased angular frequency.
No the angular frequency is independent of amplitude. .What do you mean by"multiplied through w"DR1 said:amplitude of vibration would again increase as its multiplied through w
Again look at this [tex]\omega=\sqrt{\frac{k}{m}}[/tex] angular frequency is determined ONLY by m and k in SHM. A stiffer spring is capable of applying more force on the mass remember F=-kx(again the second law). The phase only tells you at what angle your rotating vector is at t=0 so it does not effect angular frequencyDR1 said:it would have no effect on spring stiffness as i don't see any formule that use both parts but then having said that if it increases the mass that would have an effect on the sping stiffness
the phase lag would increase w as (wt+0) as such they are linked together
The mass of the object attached to the spring affects the angular frequency by changing the inertia of the system. The larger the mass, the greater the inertia, and therefore the lower the angular frequency. Similarly, a smaller mass will result in a higher angular frequency.
The spring constant, also known as the stiffness of the spring, is directly proportional to the angular frequency in a spring mass system. This means that an increase in the spring constant will result in a higher angular frequency, and vice versa.
Yes, the amplitude of the motion can affect the angular frequency in a spring mass system. A larger amplitude will result in a higher angular frequency, while a smaller amplitude will result in a lower angular frequency. This is because a larger amplitude requires more energy to maintain the motion.
The length of the spring has an inverse relationship with the angular frequency in a spring mass system. This means that a longer spring will result in a lower angular frequency, while a shorter spring will result in a higher angular frequency.
The initial position of the mass does not affect the angular frequency in a spring mass system. The angular frequency is determined by the mass, spring constant, and length of the spring, and remains constant regardless of the initial position of the mass.