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SHM Conceptual Challenge

AP Physics 1: Dynamics & Energy

CER Protocol: For all prompts marked "Justify", you must provide a Claim, mathematical Evidence, and scientific Reasoning.

1. Mass Scaling: A block-spring system oscillates with period \(T\). If the block is replaced by one with four times the mass (\(4M\)), determine the factor by which the period changes. Justify your answer using the period equation.

2. Vector Logic: An object in SHM is at position \( x = -A \). Identify the direction of the Net Force and the Acceleration. Explain your reasoning based on the directionality of restoring forces.

3. Equilibrium Velocity: Explain why the velocity of an oscillator is at its maximum magnitude when it passes through the equilibrium position (\( x = 0 \)), even though the net force at that point is zero.

4. Energy doubling: A student doubles the Amplitude of a mass-spring system from \( A \) to \( 2A \). Justify the claim that the total mechanical energy of the system increases by a factor of 4.

5. Pendulum Mass: A simple pendulum has a period of 2.0 seconds with a 1 kg bob. If the bob is replaced with a 5 kg bob, predict the new period. Explain why mass does or does not affect the timing of a pendulum.

6. Field Dynamics: A vertical mass-spring system and a simple pendulum are moved to a high-gravity planet where \( g_{new} = 4g_{earth} \). Compare the effect on their periods. Justify using the respective equations.

7. Linearity Check: An experimental spring provides a force \( F = -kx^3 \). Is this system executing Simple Harmonic Motion? Explain using the proportionality requirement of SHM.

8. Turning Point Kinematics: At \( x = +A \), describe the instantaneous velocity and acceleration. Justify why these specific values are necessary for the object to reverse its direction of motion.

9. Energy Symmetry: In a mass-spring system, at what displacement \( x \) (in terms of \( A \)) is the Kinetic Energy exactly equal to the Potential Energy? Show your algebraic derivation.

10. Graph Interpretation: Sketch a rough Force vs. Displacement graph for two springs: one with constant \( k \) and one with constant \( 2k \). Explain how the slopes of these graphs relate to the "stiffness" of the systems.

11. Pendulum Condition: Justify the requirement that a simple pendulum’s angle must remain small (\( < 15^\circ \)) to be considered Simple Harmonic Motion. What happens to the "restoring force" if the angle is too large?

12. Conservation Claim: A student claims that for a vertical spring, "Total Energy is conserved only if you pull the mass down from equilibrium." Refute or support this claim using the Law of Conservation of Energy.

SHM Conceptual Challenge Assignment

SHM Conceptual Challenge Assignment

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