# How to get max velocity for simple pendulum

• PhizKid
In summary, we are given a simple pendulum with a ball of mass 5 kg and string length of 5 m. We are asked to find the maximum velocity using the equation v = \omega \cdot A, where \omega is the angular frequency and A is the amplitude. Through solving and with the help of a friend, we find that the maximum velocity is equal to 4.43 * 0.08 * 5 = 1.774 m/s.
PhizKid

## Homework Statement

A simple pendulum has a ball at the end of mass 5 kg and the length of the string is 5 m. Given $\theta = 0.0800 \cdot cos[4.43t + \phi]$ find the maximum velocity

## Homework Equations

$\frac{1}{2}mv^2 = \frac{1}{2}kA^2$

## The Attempt at a Solution

$\frac{1}{2}mv^2 = \frac{1}{2}kA^2 \\\\ mv^2 = kA^2 \\\\ v = \sqrt{\frac{kA^2}{m}} \\\\ v = \omega \cdot A$

But the solution is $v = \omega \cdot Length \cdot A$. Why is it omega * the length * the amplitude?

EDIT: My friend helped me solve it:
w = dtheta / dt = -4.43*.08*sin(4.43t + phi)

w_max => 4.43t + phi = 3pi/2 => w_max = 4.43*.08

v_max = 4.43*.08*R = 5*4.43*.08

Last edited:
That's the one - it's what you get when you differentiate the displacement-time function: if you understand the displacement-time relationship you understand the velocity-time relationship.

## 1. What is the formula for calculating the maximum velocity of a simple pendulum?

The formula for calculating the maximum velocity of a simple pendulum is v = √(g * L * (1-cosθ)), where "v" is the maximum velocity, "g" is the acceleration due to gravity, "L" is the length of the pendulum, and "θ" is the angle between the pendulum and its resting point.

## 2. How does the length of the pendulum affect its maximum velocity?

The length of the pendulum directly affects its maximum velocity. The longer the pendulum, the greater the distance it has to travel, resulting in a higher maximum velocity. This can be seen in the formula for maximum velocity, where "L" is a factor in the calculation.

## 3. What is the relationship between the angle of release and the maximum velocity of a simple pendulum?

The angle of release has an inverse relationship with the maximum velocity of a simple pendulum. This means that as the angle of release increases, the maximum velocity decreases. This can also be seen in the formula for maximum velocity, where "θ" is a factor in the calculation.

## 4. Can the maximum velocity of a simple pendulum be greater than the initial velocity?

Yes, the maximum velocity of a simple pendulum can be greater than the initial velocity. This is because the initial velocity is only the velocity at the start of the pendulum's motion, while the maximum velocity is the highest velocity it reaches during its entire motion.

## 5. How does the mass of the pendulum affect its maximum velocity?

The mass of the pendulum does not directly affect its maximum velocity. As long as the length and angle of release are the same, the maximum velocity will remain constant regardless of the mass. However, a heavier pendulum may have a lower maximum velocity due to factors such as air resistance and friction.

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