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Date,, , , , Simple Harmonic Motion and Springs, , , , , , , , Hookean Spring Simple Harmonic Motion of Sprin;, Fy =—khx T= 2 |, —W, =U, =-4k(Ar’) kK, x = Acos(at) = Acos(2aft), i F _ kx, m m, , 1. What are the two criteria for simple harmonic motion?, , 2. The diagram to the right shows a2 kg block, attached to a Hookean spring on a frictionless, surface. The block experiences no net force when it, is at position B. When the block is to the left of, point B the spring pushes it to the right. When the, block is to the right of point B, the spring pulls it to, the left., , , , The mass is pulled to the left from point B to point A and released at time t = 0. The block then, oscillates between positions A and C. Assume that the system consists of the block and the spring and, that no dissipative forces act., , a) The block takes 40.0 s to make 20 oscillations. What is the “period of oscillation” for this system?, , b, , Whaat is the frequency of this oscillating system?, c) What is the amplitude of vibration of this system?, , d@, , Determine the spring constant of the spring., , e) Write an equation that describes the position of the mass as a function of time, starting from, position A at time t =0., , f) Explain what would happen to the period and frequency of this system if you were to double the, amplitude while keeping the mass and spring constant the same., , Explain what would happen to the period and frequency of this system if you were to double the, mass while keeping the amplitude and spring constant the same., , &, , bh, , Explain what would happen to the period and frequency of this system if you were to double the, spring constant while keeping the amplitude and mass constant., , i) Determine the amount of energy of the oscillating spring and mass system., , j) Where does the block have maximum speed and what is the maximum speed?, , k) Where does the block experience maximum acceleration and what is the maximum acceleration?, , 1) What would happen to the energy if the amplitude of oscillation were tripled while keeping the, mass and spring constant unchanged?