Hey everyone, I'm a highschool student from New Zealand and can someone please explained to me with physics principles in words:
- Why increasing the length of cantilever increases the period of oscillation?
- Why increasing the flexural rigidity of cantilever increases the period of oscillation?
- How moving the position of the attached mass effects the period of oscillation of the cantilever? (Moving closer to or further away from clamp)
The theoretical formula for the period of oscillation of a cantilever is:
$$ T=2\pi\sqrt{\frac{mL^3}{3EI}} $$
Best Answer
In words
Why increasing the length of cantilever increases the period of oscillation?
Increasing the length, for a given mass at the end, increases the deflection (Sag S). For each oscillation the distance the mass travels up and down is greater. For a wave, that means a longer wavelength (longer period of oscillation)
Why increasing the flexural rigidity of cantilever increases the period of oscillation?
That conclusion is wrong directly from the equation. The rigidity is related to the modulus of elasticity $E$ in the equation. Increasing $E$ decreases $T$. Increasing E decreases the deflection and decreases the period.
How moving the position of the attached mass effects the period of oscillation of the cantilever? (Moving closer to or further away from clamp)
Same reason as the first. Moving the mass farther away from the increases the deflection. Moving it closer decreases the deflection. It has the same effect as increasing or decreasing the length of the cantilever.
Hope this helps.