Hoop Radius for 2.0s Oscillation | SHM Object Time Calculation

In summary, the conversation is about supporting a thin hoop by a horizontal nail and making it complete one small-angle oscillation every 2.0 seconds. The question is asking for the radius of the hoop in meters. Additionally, there are several related questions about the moment of inertia, center of gravity, force due to gravity, torque, and equations for angular acceleration and the sine function. The equation for simple harmonic motion is mentioned, but more information is needed to answer the questions.
  • #1
krazy4you
2
0
We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0s .

What must the hoop's radius be (in meters) ?


and


An object is undergoing SHM with period 0.260 s and amplitude 5.55 cm. At t=0 the object is instantaneously at rest at x= 5.55 cm.

Calculate the time it takes the object to go from x= 5.55 cm to x= -1.55 cm.



SOMEONE HELP ME
 
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  • #2
krazy4you said:
We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0s .

What must the hoop's radius be (in meters) ?

what's the moment of inertia of a hoop about its center?

what's the moment of inertia of a hoop about its rim? (use parallel axis theorem)

where is the center of gravity of the hoop?

what is the force due to gravity on the hoop?

what is the torque on the hoop?

what is the equation relating torque to angular acceleration?

what is the small angle approximation for the sine function?


SOMEONE HELP ME

your caps lock key is stuck, maybe?
 
  • #3
For the second question, start with the general equation of motion of an shm. Do you know what that is?
 
  • #4
in my questions that all they gave you i need like a answer lol and some work i can't figure these two out that's all
 
  • #5
The equation describing shm is given by y=asin(wt+c), where y is the displacement, w is the angular frequency, t is time and c is the phase difference. Let's start with what you do know about shm. Any thoughts on how to go about this? Not mathematically, just conceptually.
 

FAQ: Hoop Radius for 2.0s Oscillation | SHM Object Time Calculation

1. What is oscillation?

Oscillation is a repetitive and back-and-forth movement around a central point or position. It can occur in various forms, such as in waves, pendulum motion, or vibrations.

2. What is simple harmonic motion (SHM)?

Simple harmonic motion is a type of oscillation in which the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. This results in a sinusoidal or wave-like motion.

3. What factors affect the period of oscillation in SHM?

The period of oscillation in SHM is affected by the mass of the object, the spring constant (or stiffness) of the system, and the amplitude (maximum displacement) of the oscillating object.

4. How do you calculate the frequency of oscillation?

The frequency of oscillation can be calculated by taking the inverse of the period of oscillation, which is the time it takes for one complete cycle of oscillation. The formula is: f = 1/T, where f is frequency and T is the period.

5. What is the difference between damped and undamped oscillation?

In damped oscillation, the amplitude of the oscillation decreases over time due to the dissipation of energy. This can be caused by friction, air resistance, or other external forces. In undamped oscillation, the amplitude remains constant as there is no external force dissipating the energy of the system.

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