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AP Physics 1
7.2 Frequency and Period of SHM
7.1 Defining Simple Harmonic Motion (SHM)
IntermediateMCQConceptual19.8k
Two horizontal mass-spring oscillator setups shown in a vertical stack, labeled Setup 1 and Setup 2. In Setup 1 at the top, a vertical wall on the left is attached to a horizontal coil spring of full length labeled with spring constant k, which connects to a rectangular block of mass m resting on a flat horizontal surface. A label below Setup 1 reads Period = T_0. In Setup 2 directly below, a vertical wall on the left is attached to a shorter coil spring with half as many coils, which connects to the same rectangular block of mass m on the same horizontal surface. A label below Setup 2 reads Period = T prime. No other labels, lines, text, or axes appear.
A block of mass m attached to the original spring (Setup 1) and to a half-spring (Setup 2).
A block of mass \(m\) on a frictionless horizontal surface is attached to a uniform ideal spring of force constant \(k\) and oscillates with period \(T_0\). The spring is then cut into two identical halves, and the same block is attached to one of the halves. When displaced and released, the block oscillates with a new period of \(T' = \dfrac{T_0}{\sqrt{2}}\). Which of the following statements best explains why the period decreases to this value?

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