# Ball on String, Harmonic Motion

In summary, the conversation discusses the motion of a 2.2 kg ball attached to a 0.638 m long string. The ball is pulled at an angle Θ from the vertical, raising its center of mass to a height of 0.22 m, and then released to swing down. The problem asks for the angular frequency, period, velocity of the ball when the string is vertical, and the tension in the string at that point. The solution involves using conservation of energy and solving for the velocity, resulting in a velocity of 2.08 m/s.

## Homework Statement

A 2.2 kg ball is attached to a 0.638 m long string and is pulled an angle Θ from the verticle such that the center of mass of the ball is raised a distance h=0.22 m from its lowest position. The ball is released and allowed to swing down.
a) What is the angular frequency of this motion?
b) What is the period of this motion?
c) What is the velocity of the ball when the string is vertical?
d) What is the tension in the string when it is vertical?2. The attempt at a solution

a) ω = sqrt(mgr/I) = 3.92
b) f = ω/2pi
T = 1/f = 1.603
c) I'm sure that if I could complete this I could easily find part d. I thought that I could apply conservation of energy, so I performed the following:

PEi = KEf
mgh = .5mv^2
v = sqrt(2gh)
v = sqrt(2*9.81*.22)
v = 2.0776 m/s

The software rejects this answer. I'm not sure where to go from here. Do I need to set up a differential equation to find the velocity?

Thanks!

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Your method is correct, the result is correct, but you gave it with too many significant digits. Try 2.08 (or 2.078) m/s.

ehild

## 1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which an object moves back and forth around a central equilibrium point, following a specific pattern or trajectory.

## 2. How is harmonic motion related to a ball on a string?

A ball on a string is a classic example of harmonic motion, as the ball moves back and forth in a pendulum-like motion around the point where the string is attached.

## 3. What factors affect the period of a ball on a string?

The period, or time it takes for one complete oscillation, of a ball on a string is affected by the length of the string, the mass of the ball, and the acceleration due to gravity.

## 4. How does the amplitude of a ball on a string affect its motion?

The amplitude, or maximum displacement, of a ball on a string affects its motion by determining the maximum height and speed of the ball. A larger amplitude will result in a higher maximum height and faster speed, while a smaller amplitude will have the opposite effect.

## 5. What is the relationship between the period and frequency of a ball on a string?

The period and frequency of a ball on a string are inversely related. This means that as the period increases, the frequency decreases and vice versa. This relationship is described by the equation T = 1/f, where T is the period and f is the frequency.