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?

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