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title: "A block of mass \\(M\\) is attached to a horizontal ideal spring of spring constant \\(k\\) and oscillates in simple harmonic motion on a frictionless horizontal surface with amplitude \\(A_0\\) and maximum kinetic energy \\(K_{\\text{max}, 0}\\). At the exact instant the block reaches its maximum positive displacement \\(x = +A_0\\), a small lump of clay of mass \\(m\\) is dropped vertically from rest onto the block and immediately sticks to it. How do the amplitude and the maximum kinetic energy of the subsequent simple harmonic motion of the combined system compare to \\(A_0\\) and \\(K_{\\text{max}, 0}\\), respectively?"
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url: "https://nerd-notes.com/ubq/120997/"
date_modified: "2026-08-23T04:45:03+00:00"
---

# A block of mass \(M\) is attached to a horizontal ideal spring of spring constant \(k\) and oscillates in simple harmonic motion on a frictionless horizontal surface with amplitude \(A_0\) and maximum kinetic energy \(K_{\text{max}, 0}\). At the exact instant the block reaches its maximum positive displacement \(x = +A_0\), a small lump of clay of mass \(m\) is dropped vertically from rest onto the block and immediately sticks to it. How do the amplitude and the maximum kinetic energy of the subsequent simple harmonic motion of the combined system compare to \(A_0\) and \(K_{\text{max}, 0}\), respectively?

A block of mass \(M\) is attached to a horizontal ideal spring of spring constant \(k\) and oscillates in simple harmonic motion on a frictionless horizontal surface with amplitude \(A_0\) and maximum kinetic energy \(K_{\text{max}, 0}\). At the exact instant the block reaches its maximum positive displacement \(x = +A_0\), a small lump of clay of mass \(m\) is dropped vertically from rest onto the block and immediately sticks to it. How do the amplitude and the maximum kinetic energy of the subsequent simple harmonic motion of the combined system compare to \(A_0\) and \(K_{\text{max}, 0}\), respectively?

![A schematic diagram showing a horizontal spring-mass oscillator on a flat surface. On the left is a vertical wall. A horizontal coil spring extends to the right from the wall to the left face of a rectangular block labeled M. Below the block is a horizontal ground line representing a frictionless surface. Two vertical dashed reference lines are drawn: one passing through the equilibrium position labeled x = 0, and one passing through the center of the block labeled x = +A_0. Directly above block M at x = +A_0, a small circular lump labeled m is shown with a single straight downward arrow pointing toward the top surface of block M. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460303-OkfYMB.jpg)

- **A.** Amplitude: Equal to \(A_0\) Maximum kinetic energy: Equal to \(K_{\text{max}, 0}\)
- **B.** Amplitude: Equal to \(A_0\) Maximum kinetic energy: Less than \(K_{\text{max}, 0}\)
- **C.** Amplitude: Less than \(A_0\) Maximum kinetic energy: Less than \(K_{\text{max}, 0}\)
- **D.** Amplitude: Less than \(A_0\) Maximum kinetic energy: Equal to \(K_{\text{max}, 0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120997/*