A verticle mass-spring system executed simple harmonic oscillation with a period `2 s` quantity of this system which simple varation with a period of `1sec` are

Options

A. velocity
B. potential energy
C. phese different between acceleration and displacement
D. different between kinetic energy and potential energy.

Explanation

To solve the problem regarding the vertical mass-spring system executing simple harmonic motion (SHM) with a period of 2 seconds, we need to identify which quantities vary with a period of 1 second.

### Step-by-Step Solution:

1. **Understanding the System**:
- The mass-spring system oscillates vertically and has a time period (T) of 2 seconds. This means it completes one full cycle of motion in 2 seconds.

2. **Identifying Half Period**:
- The half period (T/2) is 1 second. During this time, certain quantities will reach their maximum or minimum values.

3. **Analyzing Kinetic Energy (KE)**:
- Kinetic energy is maximum when the spring is at its equilibrium position (no displacement). It is zero at the maximum displacement (when the spring is fully stretched or compressed).
- Since KE reaches its maximum value at T/2 (1 second), it varies with a period of 1 second.

4. **Analyzing Potential Energy (PE)**:
- Potential energy is maximum at the maximum displacement (when the spring is fully stretched or compressed) and is zero at the equilibrium position.
- Similar to KE, the PE also reaches its maximum value at T/2 (1 second), indicating that it also varies with a period of 1 second.

5. **Analyzing Velocity**:
- Velocity is maximum at the equilibrium position and zero at the maximum displacement. The velocity also follows the same pattern as KE and PE, thus varying with a period of 1 second.

6. **Analyzing Acceleration**:
- Acceleration is always directed towards the equilibrium position and is maximum at maximum displacement. The acceleration varies with a period of 2 seconds, not 1 second.

7. **Conclusion**:
- The quantities that vary with a period of 1 second are:
- Kinetic Energy (KE)
- Potential Energy (PE)
- Velocity

### Final Answer:
The quantities that vary with a period of 1 second are Kinetic Energy and Potential Energy.