How Does Simple Harmonic Motion Affect Velocity and Energy in a Spring System?

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In a simple harmonic motion scenario involving a 2.6 kg block attached to a spring, the maximum velocity can be determined using the amplitude and the angular frequency derived from the sinusoidal wave properties. The mechanical energy of the system is calculated by considering both kinetic and potential energy at maximum displacement. The wave crosses the x-axis at specified intervals, indicating periodic motion, with an amplitude of 2 cm affecting the energy calculations. Analyzing the graph's characteristics is crucial for accurately determining these values. Understanding these principles is essential for grasping the dynamics of spring systems in simple harmonic motion.
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A 2.6 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above.

(a) What is maximum velocity of the box?


(b) What is the mechanical energy of the box?

now the wave is -sin wave but crosses the x-axis at 4,8,12,16,20,24 and has an amplitude of 2 cm
 
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