(i) If possible, solve for the mass of clay added at z = 0 which will halve the amplitude of oscillation. G) What is the smallest time to such that the system has equal kinetic and spring potential energy?
(i) If possible, solve for the mass of clay added at z = 0 which will halve the amplitude of oscillation. G) What is the smallest time to such that the system has equal kinetic and spring potential energy?
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Transcribed Image Text:(i) If possible, solve for the mass of clay added at \( x = 0 \) which will halve the amplitude of oscillation.
(j) What is the smallest time \( t_0 \) such that the system has equal kinetic and spring potential energy?
Transcribed Image Text:For this problem, refer to the figure below. A mass \( M \) is pulled from equilibrium at \( x = 0 \) to a position \( x = D \) and is released from rest at \( t = 0 \). The spring constant \( k \) is known. There is no friction.
**Diagram Explanation:**
The diagram illustrates a spring-mass system. It shows a block labeled \( M \) attached to a spring with a spring constant \( k \). The spring is anchored on the left side and stretched to the right. The position of the block varies along a horizontal line:
- The positions are marked from left to right as \(-D\), \(-D/2\), \(x = 0\), \(D/2\), and \(D\).
- The position \( x = 0 \) represents the equilibrium position of the spring.
- The point \( x = D \) is where the mass is initially pulled to and then released.
This setup demonstrating harmonic motion shows that the system is frictionless, allowing the mass \( M \) to oscillate back and forth when released.
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