Question

identical masses m are attached to identical springs of spring constant k suspended from the ceiling. with both masses hanging in their equilibrium positions, mass a is pulled down 10 cm and released while mass b is pushed up 10 cm and released. which statement is correct?

Answer 1

You didn't give any statements for us to pick a correct one from.

Here is a correct statement:

"There is normally more solar energy available during the daytime than there is during the night time."

Answer 2

Answer: when mass a is pulled down 10 cm and released while mass b is pushed up 10 cm and released, both masses will undergo simple harmonic motion with identical periods but with opposite phases.

Step-by-step explanation:

When mass a is pulled down 10 cm and released, it will start oscillating up and down around its equilibrium position. Similarly, when mass b is pushed up 10 cm and released, it will also start oscillating up and down around its equilibrium position. The behavior of these oscillations can be analyzed using the principles of simple harmonic motion.

In simple harmonic motion, the restoring force acting on an object is directly proportional to its displacement from the equilibrium position and acts in the opposite direction. In this case, the restoring force is provided by the springs attached to the masses.

Let's consider mass a first. When it is pulled down 10 cm and released, it will experience a restoring force from the spring that will try to bring it back to its equilibrium position. As it moves upward, the spring force decreases until it reaches its maximum displacement in the opposite direction. At this point, the spring force is at its maximum, pulling the mass back towards the equilibrium position. The mass then continues to oscillate between these two extreme positions.

The same analysis can be applied to mass b. When it is pushed up 10 cm and released, it will experience a restoring force from the spring that will try to bring it back to its equilibrium position. As it moves downward, the spring force increases until it reaches its maximum displacement in the opposite direction. At this point, the spring force is at its maximum, pushing the mass back towards the equilibrium position. The mass then continues to oscillate between these two extreme positions.

Therefore, both masses will undergo simple harmonic motion with identical periods but with opposite phases. This means that when one mass is at its maximum displacement from the equilibrium position, the other mass will be at its minimum displacement, and vice versa.

In conclusion, when mass a is pulled down 10 cm and released while mass b is pushed up 10 cm and released, both masses will undergo simple harmonic motion with identical periods but with opposite phases.