Calculating Period of Oscillation for a Colliding System

In summary, the conversation is about a problem involving a gob of clay falling and sticking to a cylinder, and the calculation of the initial angular velocity and period of oscillation of the system. The person asking for help also mentions a diagram that shows the cylinder on its side with the clay stuck to the bottom edge, and asks for further assistance, possibly involving the concept of a physical pendulum.
  • #1
SMG75
23
0
Below is a problem that I am trying to work through in preparation for an upcoming exam. I worked through part A with no problems, but I am struggling with part B. Could someone point me in the right direction?

Homework Statement



A gob of clay with mass m falls from rest a distance h before striking and sticking to the edge of a uniform cylinder of mass M and radius r. The cylinder is free to rotate about a horizontal axis through its center.

2A) What is the initial angular velocity of the cylinder with the gob of clay attached?
2B) Now assume that after the collision, the system experienced a small amount of friction such that after a long time, the system comes to undergo small periodic oscillations, as shown. Ignoring friction, calculate the period of the oscillation.

Thanks.
 
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  • #2
SMG75 said:
2B) Now assume that after the collision, the system experienced a small amount of friction such that after a long time, the system comes to undergo small periodic oscillations, as shown. Ignoring friction, calculate the period of the oscillation.

Thanks.
"As shown" where?
 
  • #3
Ah, right. I forgot to attach the diagram. It won't let me for some reason. I will try to describe it. It shows the cylinder on its side, so it just looks like a circle. The axis of rotation is in the center of that. The clay is stuck to the bottom edge, and it is making small oscillations in that manner. Any help?
 
  • #4
Does "physical pendulum" ring a bell?
 
  • #5


For part B, you will need to use the concept of conservation of energy and the equation for the period of a simple harmonic oscillator. First, calculate the total energy of the system before and after the collision, taking into account the potential energy of the clay and the kinetic energy of the cylinder. Then, use the equation T = 2π√(m/k) where m is the reduced mass of the system (mM/(m+M)) and k is the effective spring constant (derived from the conservation of energy equation). This will give you the period of the oscillation. Remember to ignore the effect of friction in your calculations. I hope this helps!
 

1. What is the period of oscillation?

The period of oscillation is the time it takes for an oscillating object to complete one cycle of its motion. It is measured in seconds (s).

2. How is the period of oscillation related to frequency?

The period of oscillation is inversely proportional to the frequency of the oscillation. This means that as the period increases, the frequency decreases, and vice versa. This relationship can be mathematically represented by the equation T = 1/f, where T is the period and f is the frequency.

3. What factors affect the period of oscillation?

The period of oscillation is affected by the mass, stiffness, and length of the oscillating object. A heavier object will have a longer period, while a stiffer or shorter object will have a shorter period.

4. How does the amplitude of oscillation affect the period?

The amplitude of oscillation, or the maximum displacement from the equilibrium position, does not affect the period. The period is only dependent on the physical properties of the oscillating object and is not affected by its amplitude.

5. Can the period of oscillation be changed?

Yes, the period of oscillation can be changed by altering the physical properties of the oscillating object. For example, changing the mass, stiffness, or length of the object can change its period. Additionally, the period can also be changed by external forces, such as friction or air resistance, which can affect the motion of the object.

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