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Unformatted text preview: 1 Motion that repeats itself is ____________ motion. Simple harmonic motion is typically what we see when we _________ an object from equilibrium. The time that it takes to make one complete repetition or cycle is called the ____________ , T,of the motion. Oscillations Chapter 14 ____________ is the maximum distance the mass moves from its equilibrium position. It moves as far on one side as it does on the other. SHO definitions ___________________ , f, is the number of cycles per second that an oscillator goes through. Frequency is measured in "hertz" which means cycles per second. f =1/T The _______________ FREQUENCY is measured in radians per second. To convert that to periods per second or cycles per second, we need is measured in _____________per second. T 2 f 2 = = SHO definitions According to Hookes Law, the restoring force exerted by the spring is F = _____________ So the net force on our Simple Harmonic Oscillator (SHO), expressed in terms of Newtons second law, is F net = -k x = ma = m d 2 x/dt 2 d 2 x/dt 2 = ________________ OR a = -(k/m) x How do we solve for the position of the mass on the spring? We use the time-honored technique of guessing and "guess" a solution with the form of x = _______________________ Newtons 2 nd Law Applied to SHO 2 x = A cos(C t) We must ensure that this is a solution and determine what the constant C is. In order to do this we must take the first and second derivatives of our guess. Taking the derivatives: dx/dt= ________________ d 2 x/dt 2 = ___________________ But that means d 2 x/dt 2 = _______________ and we already know d 2 x/dt 2 = -(k/m) x Newtons 2 nd Law Applied to SHO d 2 x/dt 2 = -C 2 [ x ] and d 2 x/dt 2 = -(k/m) x So that requires C 2 = __________ OR We call this constant , which is the angular frequency. That means we can write our solution as x = A cos( t) Newtons 2 nd Law Applied to SHO _______________ The equations of motion for Simple Harmonic Oscillators are...
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