# How the length, flexural rigidity and position of attached mass affects the period of oscillaion of cantilever?

Hey everyone, I'm a highschool student from New Zealand and can someone please explained to me with physics principles in words:

1. Why increasing the length of cantilever increases the period of oscillation?
2. Why increasing the flexural rigidity of cantilever increases the period of oscillation?
3. 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: $$T=2\pi\sqrt{\frac{mL^3}{3EI}}$$

• The answers to your 3 questions could be deduced from the given formula. Do you ask for an explanation about how to deduce this? Or do you ask for how to arrive at this formula? – Thomas Fritsch May 22 at 9:55
• FYI, rigidity is reducing the period according to that formula. – JMac May 22 at 11:23

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.

• Thank you sir. Do you mind answering the latest question I posted? – Matthew May 28 at 10:42
• Was this answer acceptable for this post! – Bob D May 28 at 11:15