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A block with mass M attached to a horizo...

A block with mass `M` attached to a horizontal spring with force constant `k` is moving with simple harmonic motion having amplitude `A_(1)`. At the instant when the block passes through its equilibrium position a lump of putty with mass `m` is dropped vertically on the block from a very small height and sticks to it.
(a) Find the new amplitude and period.
(b) Repeat part (a) for the case in which the putty is dropped on the block when it is at one end of its path.

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To solve the problem step by step, we will break it down into two parts as requested: ### Part (a): Putty Dropped at Equilibrium Position 1. **Initial Conditions**: - The mass of the block is \( M \). - The spring constant is \( k \). - The initial amplitude of the block's motion is \( A_1 \). ...
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