Calculate the amplitude (maximum displacement from equilibrium) of the motion. What is the oscillation frequency, ω, of the mass? Please also include what the maximum acceleration of the mass as it oscillates.

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Calculate the amplitude (maximum displacement from equilibrium) of the motion. What is the oscillation frequency, ω, of the mass? Please also include what the maximum acceleration of the mass as it oscillates.

 

You place a mass \( m = 2 \, \text{kg} \) on a frictionless horizontal surface, and attach it to a wall with a spring as shown below. The spring has spring constant \( k = 1000 \, \text{N/m} \).

The mass sits at \( x = 0 \) in equilibrium. At time \( t = 0 \), you give the mass a whack, sending it moving to the right with an instantaneous velocity of \( v_0 = 3 \, \text{m/s} \) at \( x = 0 \), and the mass begins to undergo simple harmonic motion.

**Diagram Explanation:**

The diagram illustrates a block of mass \( m \) attached to a spring. The spring is connected to a wall on one end, while the other end is attached to the block. The block is labeled with \( m \), and the spring is labeled with \( k \) to signify the spring constant. The surface beneath the block is horizontal and frictionless, depicted as a flat surface. The layout reflects that the block can only move horizontally.

This setup forms a classic physics problem involving simple harmonic motion, where the spring's force provides the restoring force that causes the oscillation of the mass.
Transcribed Image Text:You place a mass \( m = 2 \, \text{kg} \) on a frictionless horizontal surface, and attach it to a wall with a spring as shown below. The spring has spring constant \( k = 1000 \, \text{N/m} \). The mass sits at \( x = 0 \) in equilibrium. At time \( t = 0 \), you give the mass a whack, sending it moving to the right with an instantaneous velocity of \( v_0 = 3 \, \text{m/s} \) at \( x = 0 \), and the mass begins to undergo simple harmonic motion. **Diagram Explanation:** The diagram illustrates a block of mass \( m \) attached to a spring. The spring is connected to a wall on one end, while the other end is attached to the block. The block is labeled with \( m \), and the spring is labeled with \( k \) to signify the spring constant. The surface beneath the block is horizontal and frictionless, depicted as a flat surface. The layout reflects that the block can only move horizontally. This setup forms a classic physics problem involving simple harmonic motion, where the spring's force provides the restoring force that causes the oscillation of the mass.
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