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Welcome to our Physics lesson on Velocity and Acceleration in a Simple Harmonic Motion, this is the fifth lesson of our suite of physics lessons covering the topic of Simple Harmonic Motion, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
From calculus it is known that the first derivative of position with respect to time (dx/dt) represents the velocity v and the second derivative of position with respect to time d2x/dt2 (or the first derivative of velocity in respect to time dv/dt) gives the acceleration a.
Also, the first derivative of sin x is equal to cos x and the first derivative of cos x = - sin x. Likewise, the first derivative of k × sin a × x = k × a × cos a × x and the first derivative of k × a × cos a × x = - k × a2 × sin a × x.
Applying the above derivation rules for the SHM motion, we obtain for the velocity v in respect to the time, v(t):
and for the acceleration a in respect to the time, a(t):
Therefore, we obtained a very important formula of SHM that relates acceleration a, angular frequency ω and displacement x:
You have reached the end of Physics lesson 10.1.5 Velocity and Acceleration in a Simple Harmonic Motion. There are 6 lessons in this physics tutorial covering Simple Harmonic Motion, you can access all the lessons from this tutorial below.
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