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Consider a mass m that oscillates without damping on a spring with Hooke's constant k, so that its position function x(t) satisfies the differential equation x" + w²x = 0 (where w? = k/m). If we introduce the velocity y = dx/dt of the mass, we get the system dx = y, dt dy -w?x dt

Consider a mass m that oscillates without damping on a spring with Hooke's constant k, so that its position function x(t) satisfies the differential equation x" + w²x = 0 (where w? = k/m). If we introduce the velocity y = dx/dt of the mass, we get the system dx = y, dt dy -w?x dt

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Consider a mass m that oscillates without damping on a spring with Hooke's constant k, so that its position function x(t) satisfies the differential equation x" + w²x = 0 (where w? = k/m). If we introduce the velocity y = dx/dt of the mass, we get the system dx = y, dt dy -w?x dt
Transcribed Image Text:Consider a mass m that oscillates without damping on a spring with Hooke's constant k, so that its position function x(t) satisfies the differential equation x" + w²x = 0 (where w? = k/m). If we introduce the velocity y = dx/dt of the mass, we get the system dx = y, dt dy -w?x dt
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