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As the block initially moves from z =D toward r = 0, does the spring force do positive, negative, or zero work? When the block is at z = D, I slap a hunk of clay straight down (that is, with no horizontal velocity) onto the mass and it sticks. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? The system is reset to t = 0. This time, I add the clay when the block passes through z = 0. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation?

As the block initially moves from z =D toward r = 0, does the spring force do positive, negative, or zero work? When the block is at z = D, I slap a hunk of clay straight down (that is, with no horizontal velocity) onto the mass and it sticks. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? The system is reset to t = 0. This time, I add the clay when the block passes through z = 0. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation?

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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 horizontal spring-mass system. It shows a mass \( M \) attached to a spring with constant \( k \). The spring is fixed on one end and extended to position \( x = D \) on the other. The mass is initially at rest. The positions labeled along the horizontal axis are \( -D \), \(-D/2 \), \( x = 0 \) (equilibrium position), \( D/2 \), and \( D \).
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 horizontal spring-mass system. It shows a mass \( M \) attached to a spring with constant \( k \). The spring is fixed on one end and extended to position \( x = D \) on the other. The mass is initially at rest. The positions labeled along the horizontal axis are \( -D \), \(-D/2 \), \( x = 0 \) (equilibrium position), \( D/2 \), and \( D \).
(e) As the block initially moves from \( x = D \) toward \( x = 0 \), does the spring force do positive, negative, or zero work? (f) When the block is at \( x = D \), I slap a hunk of clay straight down (that is, with no horizontal velocity) onto the mass and it sticks. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? (g) The system is reset to \( t = 0 \). This time, I add the clay when the block passes through \( x = 0 \). Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? (h) If possible, solve for the mass of clay added at \( x = 0 \) which will double the period of oscillation.
Transcribed Image Text:(e) As the block initially moves from \( x = D \) toward \( x = 0 \), does the spring force do positive, negative, or zero work? (f) When the block is at \( x = D \), I slap a hunk of clay straight down (that is, with no horizontal velocity) onto the mass and it sticks. Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? (g) The system is reset to \( t = 0 \). This time, I add the clay when the block passes through \( x = 0 \). Does the amplitude of oscillation increase, decrease, or neither? What about the period of oscillation? (h) If possible, solve for the mass of clay added at \( x = 0 \) which will double the period of oscillation.
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