For a linear SHM when the distance of the oscillator from the equilibrium position has values y₁ and y₂, the velocities v₁ and v₂. Show that the time period of oscillation is T = 2π [(y₂² - y₁²)/(v₁² - v₂²)]⁽¹/²⁾.
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Answer:
harmonic motion
Describe the motion of a mass oscillating on a vertical spring
When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time ((Figure)). The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing. In this section, we study the basic characteristics of oscillations and their mathematical description.
A photograph of a guitar being played.
Figure 15.2 When a guitar string is plucked, the string oscillates u