Question
A particle moves on the X-axis according to the equation x=A+Bsinω t. The motion is simple harmonic with amplitude.
Answer: Option B
:
B
We are given x=A+Bsinωt
We can see that the second term basically is the equation of an SHM with amplitude B. What's the first term doing there? Let's think about it. If it were just B sin ωt, it would be an SHM about the origin. Adding a constant to this entire thing would just shift the mean position from origin to x = A. Now the particle is doing SHM about x = A with an amplitude of B. Yes B! because amplitude is how far the particle goes from the mean position. The new means position is x = A but the particle's max displacement is still B from it!
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:
B
We are given x=A+Bsinωt
We can see that the second term basically is the equation of an SHM with amplitude B. What's the first term doing there? Let's think about it. If it were just B sin ωt, it would be an SHM about the origin. Adding a constant to this entire thing would just shift the mean position from origin to x = A. Now the particle is doing SHM about x = A with an amplitude of B. Yes B! because amplitude is how far the particle goes from the mean position. The new means position is x = A but the particle's max displacement is still B from it!
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