Oscillations of a weighted ruler

[qazxsw11111]

Hi everyone. Can you imagine a metre rule attached to a tabletop and weights are attached at the other end? The ruler will sag. The ruler is then given a push to let it oscillate. However the weights fell off when it is oscillating. So what is the effect on period and amplitude?

I did:

Since w=sqrt of k/m, when m decreases w decreases.
w=2pi/t, thus t will increase.

However, although i cannot think of any equation that affects the amplitude (I think it is constant), but my answer script says that amplitude actually increased. Can anyone use equations to prove that to me?

Thank you!

 

[Nate810]

The equation that affects the amplitude is the equation of simple harmonic motion. This equation states that the amplitude of the oscillation is equal to the maximum displacement of the particle. Since the weights had fallen off, the maximum displacement will increase leading to an increase in the amplitude.

 

[nlightner]

I would like to clarify that the equations you have mentioned are correct in explaining the effect of the weights falling off on the period and frequency of oscillation. However, the effect on amplitude is not as straightforward and cannot be determined solely by equations.

The amplitude of an oscillation is determined by the initial conditions of the system, including the initial displacement and velocity. In this case, the weights falling off would change the initial conditions of the system, leading to a different amplitude.

To prove that the amplitude would increase, we would need to consider the conservation of energy in the system. When the weights fall off, the potential energy of the system decreases, but the total energy (which is the sum of potential and kinetic energy) remains constant. This means that the kinetic energy of the system must increase, leading to a larger amplitude of oscillation.

Furthermore, the weights falling off would also affect the damping of the system, which can also impact the amplitude of oscillation. Without the weights, there may be less damping in the system, allowing for a larger amplitude.

Therefore, while equations can explain the effect of the weights falling off on the period and frequency of oscillation, the change in amplitude cannot be determined solely by equations and would require a more detailed analysis of the system.