When an object is moving in a simple harmonic motion, which of the following is at a minimum when the displacement from equilibrium is zero?
A. the magnitude of the velocity
B. the magnitude of the acceleration
C. the kinetic energy
D. the total mechanical energy
E. More than one of the above answers.
acceleration, since velocity is max at x=0.
Well, well, well, looks like we have a simple harmonic motion enthusiast in the house! Let's have some fun with this question, shall we?
When the displacement from equilibrium is zero, it means that our little object is right smack in the middle of its motion. Now, let's take a look at the options:
A. The magnitude of the velocity: Picture this - the object is right in the middle, not moving at all. So, its velocity would be zero, right? Ding ding ding, we found our minimum!
B. The magnitude of the acceleration: Now, think about it. If the object is right in the middle, it must be neither speeding up nor slowing down. So, the acceleration should also be zero. Nope, not our minimum.
C. The kinetic energy: Now, here's a tricky one. Kinetic energy is related to velocity, and since the object is not moving when it's at equilibrium, its kinetic energy should also be zero. Another bingo!
D. The total mechanical energy: This includes both kinetic and potential energy. But remember, when the object is in equilibrium, its velocity and displacement are zero, meaning both forms of energy should be at their minimum. Oh baby, we got another winner!
So, after all the clowning around, it turns out that more than one of the above answers is correct - both A and C! Give yourself a pat on the back for cracking that joke of a question. Keep up the harmonious spirit, my friend!
When the displacement from equilibrium is zero in a simple harmonic motion, the object is at its equilibrium position.
For an object in simple harmonic motion, at its equilibrium position, the magnitude of the velocity is at a maximum and the magnitude of the acceleration is at a minimum.
Therefore, the correct answer is:
B. The magnitude of the acceleration
To determine which of the given options is at a minimum when the displacement from equilibrium is zero in a simple harmonic motion, we need to understand the characteristics of simple harmonic motion.
In simple harmonic motion, the displacement of an object from its equilibrium position can be represented by a sinusoidal function. When the displacement is zero, the object is at its equilibrium position.
Now let's consider each option:
A. The magnitude of the velocity: Velocity measures the rate of change of displacement with respect to time. When the displacement is zero, the object is momentarily at rest, so the velocity is at a minimum.
B. The magnitude of the acceleration: Acceleration measures the rate of change of velocity with respect to time. When the displacement is zero, the object is momentarily at rest, so the acceleration is also at a minimum.
C. The kinetic energy: Kinetic energy depends on the mass and velocity of an object. When the displacement is zero, the object is momentarily at rest, so the velocity is zero, and consequently, the kinetic energy is at a minimum.
D. The total mechanical energy: Total mechanical energy is the sum of potential energy and kinetic energy. When the displacement is zero, the object is momentarily at rest, so the kinetic energy is at a minimum. Since potential energy is zero at equilibrium, the total mechanical energy is also at a minimum.
Considering the explanations above, we can see that options A, B, C, and D are all at a minimum when the displacement from equilibrium is zero in simple harmonic motion. Therefore, the answer is E. More than one of the above answers.