Question

How do you determine the max positive/ negative acceleration, max positive velocity, max kinetic and potential energy in (x vs t) oscillation graph that have the same amplitude?

Answer 1

To determine the maximum positive and negative acceleration, maximum positive velocity, and maximum kinetic and potential energy in an x vs. t oscillation graph with the same amplitude, you can analyze the properties of the graph and apply the principles of simple harmonic motion (SHM).

1. Maximum positive and negative acceleration: The maximum positive and negative accelerations occur when the displacement of the oscillating object is at its maximum (amplitude) points. At these points, the object is undergoing maximum acceleration due to the restoring force acting on it. The acceleration is directed towards the equilibrium position. Thus, the maximum positive and negative accelerations are equal in magnitude, but have opposite signs.

2. Maximum positive velocity: The maximum positive velocity occurs at the equilibrium position (where the displacement is zero) in an x vs. t oscillation graph. At this point, the object reaches its maximum positive velocity as it passes through the equilibrium position. The velocity decreases as the object moves away from the equilibrium position.

3. Maximum kinetic energy: The maximum kinetic energy occurs when the object is at its maximum displacement (amplitude) points in the x vs. t oscillation graph. At these points, the object has zero potential energy and maximum kinetic energy since it is moving with its maximum velocity. The kinetic energy is given by the equation K.E. = (1/2) * m * v^2, where m is the mass of the object and v is its velocity.

4. Maximum potential energy: The maximum potential energy occurs at the equilibrium position in an x vs. t oscillation graph. At this point, the object has zero kinetic energy and maximum potential energy. As the object moves away from the equilibrium position, the potential energy decreases and gets converted into kinetic energy.

In summary, the key points in an x vs. t oscillation graph with the same amplitude are as follows:

• Maximum positive and negative acceleration occur at the maximum displacement points (amplitude).
• Maximum positive velocity occurs at the equilibrium position (zero displacement).
• Maximum kinetic energy occurs at the maximum displacement points (amplitude).
• Maximum potential energy occurs at the equilibrium position (zero displacement).