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You are watching an object that is moving in SHM. When the
Chapter 14, Problem 31E(choose chapter or problem)
You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20 m/s to the right and an acceleration of 8.40 m/s2 to the left. How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?
Questions & Answers
QUESTION:
You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20 m/s to the right and an acceleration of 8.40 m/s2 to the left. How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?
ANSWER:Solution 31E Step 1: We know the equation for the SHM, X = A sin t Where, A - Amplitude of the motion - Angular velocity t - Time Taking the first derivative of X with respect to time we get, dX/dt = A cost This is nothing but the velocity. So, v = A cost Taking the second derivative of X with respect to time we get, 2 2 2 d X/dt = - A sin t 2 This is nothing but the acceleration of the motion. So, a = - A sin t