The function (sin ωt – cos ωt) represents(a) a simple harmonic motion with a period π/ω.(b) a simple harmonic motion with a period 2π/ω.(c) a periodic, but not simple harmonic motion with a period π/ω.(d) a periodic, but not simple harmonic motion with a period 2π/ω
Question
The function (sin ωt – cos ωt) represents(a) a simple harmonic motion with a period π/ω.(b) a simple harmonic motion with a period 2π/ω.(c) a periodic, but not simple harmonic motion with a period π/ω.(d) a periodic, but not simple harmonic motion with a period 2π/ω
Solution
The function (sin ωt – cos ωt) represents a periodic, but not simple harmonic motion with a period 2π/ω. So, the correct answer is (d) a periodic, but not simple harmonic motion with a period 2π/ω.
Here's why:
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The function is a combination of two simple harmonic motions (sin ωt and -cos ωt), each with a period of 2π/ω.
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The combination of these two motions results in a motion that is still periodic (it repeats over time), but it is not a simple harmonic motion (it doesn't follow the simple sine or cosine wave pattern).
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The period of the resulting motion is still 2π/ω, because that's the period of the individual motions that make it up.
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