7. Two identical masses, each of mass m, are connected to the same point on the ceiling by ideal strings of length L. The string of the first mass makes and angle 0 with the vertical, while the second mass hangs vertically. Both are initially at rest. The first mass is released, swings through angle 0, and has a completely inelastic collision with the second mass. Find the frequency of the oscillation and the maximum angular displacement after the collision. m Cma there are tuo massls here!

Elements Of Electromagnetics
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Can someone please explain it to me ASAP?!!! This is periodic motion
### Physics Problem: Oscillatory Motion with Collision

**Problem Statement:**

Two identical masses, each of mass \( m \), are connected to the same point on the ceiling by ideal strings of length \( L \). The string of the first mass makes an angle \( \theta \) with the vertical, while the second mass hangs vertically. Both are initially at rest. The first mass is released, swings through angle \( \theta \), and has a completely inelastic collision with the second mass. Find the frequency of the oscillation and the maximum angular displacement after the collision.

**Diagram Description:**

The diagram illustrates a setup of two pendulums:

- The first pendulum, with mass \( m \), is shown at an initial angle \( \theta \) from the vertical.
- The second pendulum, also with mass \( m \), hangs straight down vertically.
- Both pendulums are attached to the same fixed point on the ceiling with strings of equal length \( L \).

There is an annotation pointing out that "there are two masses here!"

**Key Points:**

1. Initially, both masses are at rest.
2. The first mass swings down due to gravity when released.
3. Upon collision, the first mass undergoes a completely inelastic collision with the second mass.
4. Post-collision, we are to determine:
   - The frequency of oscillation of the combined system.
   - The maximum angular displacement immediately following the collision.

### Solution Approach

1. **Conservation of Momentum:** Since the collision is completely inelastic, use the conservation of linear momentum to find the velocity of the combined masses right after the collision.
2. **Oscillatory Motion Analysis:** Analyze the subsequent motion of the combined masses as a simple pendulum to find the frequency and maximum angular displacement.

This educational problem requires the application of principles from mechanics, including conservation of momentum and the analysis of pendulum motion, to derive the solution.
Transcribed Image Text:### Physics Problem: Oscillatory Motion with Collision **Problem Statement:** Two identical masses, each of mass \( m \), are connected to the same point on the ceiling by ideal strings of length \( L \). The string of the first mass makes an angle \( \theta \) with the vertical, while the second mass hangs vertically. Both are initially at rest. The first mass is released, swings through angle \( \theta \), and has a completely inelastic collision with the second mass. Find the frequency of the oscillation and the maximum angular displacement after the collision. **Diagram Description:** The diagram illustrates a setup of two pendulums: - The first pendulum, with mass \( m \), is shown at an initial angle \( \theta \) from the vertical. - The second pendulum, also with mass \( m \), hangs straight down vertically. - Both pendulums are attached to the same fixed point on the ceiling with strings of equal length \( L \). There is an annotation pointing out that "there are two masses here!" **Key Points:** 1. Initially, both masses are at rest. 2. The first mass swings down due to gravity when released. 3. Upon collision, the first mass undergoes a completely inelastic collision with the second mass. 4. Post-collision, we are to determine: - The frequency of oscillation of the combined system. - The maximum angular displacement immediately following the collision. ### Solution Approach 1. **Conservation of Momentum:** Since the collision is completely inelastic, use the conservation of linear momentum to find the velocity of the combined masses right after the collision. 2. **Oscillatory Motion Analysis:** Analyze the subsequent motion of the combined masses as a simple pendulum to find the frequency and maximum angular displacement. This educational problem requires the application of principles from mechanics, including conservation of momentum and the analysis of pendulum motion, to derive the solution.
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