# Calculating Average Velocity in Spring-Mass System

• UrbanXrisis
In summary, a spring-mass system is a physical system that consists of a mass attached to a spring, creating a simple harmonic motion. The average velocity in this system can be calculated by dividing the total displacement by the total time taken for the motion, and is typically measured in meters per second (m/s). The average velocity can be negative, indicating that the mass is moving in the opposite direction of the displacement. The mass does not directly affect the average velocity, but a larger mass may result in a slower average velocity due to its greater inertia.
UrbanXrisis
A spring-mass system moves according to the position function x(t)=Asint. What is the average velocty in the period 0<=t<=2s?

so the velocity is $$v(t)=A \omega cost$$
how would I calculate the average velocity?

$$\frac{A \omega cost |^2_0}{2}$$ ??

Definition for the average velocity

$$\bar{v}_{T}=\frac{1}{T}\int_{0}^{T} v(t) \ dt$$

Daniel.

I get:
$$\frac{\int_0^2Acost}{2}$$
$$\frac{Acos2-A}{2}$$

$$\int \cos t \ dt =\sin t +C$$

Daniel.

## 1. What is a spring-mass system?

A spring-mass system is a physical system that consists of a mass attached to a spring. The mass can move back and forth due to the force of the spring, creating a simple harmonic motion.

## 2. How do you calculate the average velocity in a spring-mass system?

The average velocity in a spring-mass system can be calculated by dividing the total displacement of the mass by the total time taken for the motion. This can be represented by the formula: average velocity = total displacement / total time.

## 3. What is the unit of measurement for average velocity in a spring-mass system?

The unit of measurement for average velocity in a spring-mass system is meters per second (m/s). This is because velocity is a vector quantity that measures the rate of change of displacement over time, and it is typically measured in meters per second.

## 4. Can average velocity be negative in a spring-mass system?

Yes, the average velocity in a spring-mass system can be negative. This indicates that the mass is moving in the opposite direction of the displacement. For example, if the mass starts at a positive displacement and ends at a negative displacement, the average velocity will be negative.

## 5. How does the mass affect the average velocity in a spring-mass system?

The mass does not directly affect the average velocity in a spring-mass system. The average velocity is determined by the total displacement and time, which are both affected by the amplitude and frequency of the motion. However, a larger mass may result in a slower average velocity due to its greater inertia and resistance to motion.

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